Following the sacking of Jose Mourinho in December 2018, Ole Gunnar Solskjaer came in as a stop-gap arrangement and transformed the fortunes of a faltering Manchester United.After a disastrous start to the 2018-19 season, Manchester United climbed up the league table under Solskjaer. They also overcame a 2-0 first-leg deficit at home to beat Paris St. Germain in the Champions League Round of 16.After winning 14 of his 19 matches in charge of the club, Solskjaer was appointed the permanent manager of Manchester United. However, since then, the Norwegian's Midas touch has been on the wane.Despite leading Manchester United to a creditable third-place finish in the Premier League last season, Solskjaer's men have blown hot and cold this season.The Old Trafford club failed to win their first three league games at home in a season for the first time in almost five decades. Manchester United have also endured three defeats in ten games to lie five points off Premier League leaders Tottenham Hotspur.In the Champions League, Manchester United lost three of their last four games to slip from first to third in their group and miss out on the Round of 16. Solskjaer has now lost five of his nine games in the competition while in charge of the English club.5 - Ole Gunnar Solskjær has lost five of his nine UEFA Champions League matches as a manager (W4); no manager has been defeated six or more times in their first 10 games in the competition while in charge of English sides. Worry. pic.twitter.com/kG4eMcyU7N— OptaJoe (@OptaJoe) December 8, 20205 managers who could replace Manchester United manager Ole Gunnar SolskjaerAlthough Champions League elimination and a loss in the upcoming Manchester derby is unlikely to cost Solskjaer his job, Manchester United need to rediscover their mojo during the busy Christmas/New Year festive period to break into the top four.However, if the club's indifferent form doesn't improve under Solskjaer, it is likely that the Norwegian could be relieved of his duties. On that note, let us have a look at five managers who could replace Ole Gunnar Solskjaer at the helm of Manchester United.#5 Andre Villas-BoasAndre Villas-BoasAndre Villas-Boas is one of the most promising young tacticians in the game.After winning the Primeira Liga and the Europa League with Porto, Villas-Boas arrived at Chelsea in the summer of 2011. However, unlike his illustrious predecessor and former Manchester United manager Jose Mourinho, the young Portuguese did not last the entire season at the English club.He had better luck in his next managerial stint at Tottenham Hotspur, garnering 72 points - a record tally for a Premier League club not finishing in the top four. However, after the sale of Gareth Bale, Spurs' form nosedived and Villas-Boas was out of a job by December.2007 - André Villas-Boas is the 1st non-temporary manager to lose his 1st game with Marseille in Ligue 1 since Éric Gerets v St Etienne in October 2007 (0-1). Surprise. pic.twitter.com/5WC3QpkbUf— OptaJean (@OptaJean) August 10, 2019The Portuguese tactician then had stints at Zenit St. Petersburg and Shanghai before arriving at Marseille last summer.Villas-Boas made good use of the limited resources at his disposal to take Marseille to the Champions League for the first time in seven years. Despite the club's European elimination, Marseille are within touching distance of the Ligue 1 summit.At Manchester United, Villas-Boas will have an array of options to choose from. With his prior experience of managing in the Premier League, the 43-year-old could be a good option in case Manchester United decide to give Solskjaer the boot.#4 Thomas TuchelThomas TuchelParis Saint Germain manager Thomas Tuchel could be another contender for the Manchester United top job if Ole Gunnar Solskjaer ceases to remain at the Old Trafford club's helm.The German tactician could be available as early as next summer, as his contract at the French club runs out at the end of the season.Tuchel is no stranger to title ambitions at a top club. During his previous managerial stint at Borussia Dortmund, he won the first trophy of his career by leading BVB to the 2017-18 DFB Pokal title.Since his arrival in Paris, Tuchel has done a decent job, winning back-to-back league titles and leading PSG to their first Champions League final last season.The 47-year-old has displayed impressive tactical flexibility and man-management prowess. With no shortage of 'stars' at Old Trafford, Tuchel's experience of managing the egos of big-name players like Kylian Mbappe, Neymar and Angel Di Maria at PSG could come in handy.With Manchester United still looking for their first Premier League title in the post-Sir Alex Ferguson era, there could be no better man than Tuchel to help the club end their long league drought.0 - Paris have failed to score in their last three all competitions games, a first since November 2011 (3). It is also one time more than Thomas Tuchel's first 103 games as PSG's manager. Danger ? pic.twitter.com/Dr69tI60Vc— OptaJean (@OptaJean) September 14, 2020However, Tuchel's job at PSG is in no immediate danger, as the Ligue 1 leaders turned around their indifferent start to their Champions League campaign to reach the Round of 16.