The 25-year-old has spent one season in the Chinese Super League after joining from Atletico Madrid in February 2018.
However, both Arsenal and United are looking to bolster their squads with a new attacking signing during the January transfer window.
Sky Italia is reporting that Carrasco is considered as a potential option by both Premier League clubs.
The report also claimed that AC Milan are interested in Carrasco, but the Belgium international is understood to favour a move to Arsenal.
Carrasco joined Dalian Yifang for £26.5 million last year and the Chinese club, who finished 11th in the table last season, will want to recoup that fee.
Carrasco made an immediate impact on the left side of Dalian Yifang’s attack with seven goals and five assists in 25 appearances.
The 25-year-old is also capable of playing a more defensive role and has been used as a wing-back by Roberto Martinez for Belgium’s national team.
