The 31-year-old has just one year remaining on his contract with the Blues, rsising questions over his future with the club.
Alonso joined Chelsea from Fiorentina for £24 million in 2016. He has made over 210 appearances for the club across competitions, including 46 last season.
He has won a Premier League, Champions League, Europa League, FIFA Club World Cup, and FA Cup title with the club but lost his place to Ben Chilwell last season.
However, the England international suffered a season-ending knee-injury in November, which resulted in Alonso becoming a regular starter once again.
He scored five goals last season as Tuchel's side reached the FA Cup and EFL Cup finals and finished third in the Premier League.
Despite his prominent role with the Bluee, Alonso is still interested in a move back to his home country.
"I have one more year of my contract. I have already said it other time that I would like it, but in the end it does not depend entirely on me. It is clear that the desire to one day play in Spain is there," said Alonso as per Radioestadio Noche.
Chelsea view Marc Cucurella as Marcos Alonso replacement
According to The Sun, Chelsea are interested in Brighton & Hove Albion left-back Marc Cucurella.
He joined Brighton from Getafe last summer. His defensive solidity and ability to contribute in attack helped the Seagulls finish ninth in the Premier League, their best finish in England's top flight. He was awarded Brighton's 'Player of the Season'.
The Spaniard's technical ability could make him an ideal replacement for Alonso. Brighton could demand a fee in the region of £45 million for the 23-year-old.