The 22-year-old has hugely impressed for Patrick Vieira's Palace this season and earned an England international call-up this week.
His performances have drawn the attention of the Premier League's big guns and, according to the Daily Mail, they will also look to target the defender this summer.
Pep Guardiola is reportedly on the lookout for a new left-back to challenge Oleksandr Zinchenko.
He will have competition, however, from Chelsea and Tottenham, who both like the look of the Palace youngster.
Mitchell made the breakthrough into the first-team at Selhurst Park last season, having made his senior debut back in 2020.
The promising talent has made 32 appearances, contributing two assists and has played an important role in Crystal Palace's impressive season.
The Eagles left-hand side is a constant nuisance for the opposition, with Palace's star man Wilfried Zaha flourishing in front of Mitchell.
Mitchell's defensive talents have been lauded by his teammates.
Zaha spoke following Palace's 1-1 draw on the defensive capabilities of Mitchell, telling the club's official website:
“To be honest, that’s what I expect from (Tyrick), When I have conversations with him, we don’t even talk about his defensive aspect. I just tell him to be more confident going forwards because defensively he’s probably one of the best."
Mitchell is a product of Brentford's youth academy and has shown maturity beyond his years since being bedded into the first-team at Palace.
Should Mitchell head to Manchester City, Chelsea or Tottenham Hotspur?
The youngster continues to impress with every performance and will be looking to get inducted in Gareth Southgate's new generation of young talents for England.
Mitchell's pace and defensive capabilities alongside his attacking nuance could prove hugely beneficial for Manchester City, especially with Zinchenko their only natural option at left-back.
Chelsea have Ben Chilwell and Marcos Alonso currently vying for the left-back position at Stamford Bridge.
Chilwell, however, is out injured having incurred a knee ligament injury back in November and it is unknown when he'll return for Chelsea.
Alonso has filled in for the time being but perhaps Thomas Tuchel feels there's a need to look to the future with Alonso now at the age of 31. The Italian defender's contract expires next year.
Tottenham Hotspur have Sergi Reguilon, Ryan Sessegnon and Ben Davies at left back.
Reguilon could depart this summer having been linked with a move to Barcelona per SPORT.
Sessegnon has not lived up to expectations, having flourished for Fulham prior to joining Tottenham.
Mitchell has a huge future and it will be interesting to see who among City, Chelsea or Tottenham move for him this summer.