The 29-year-old moved to Chelsea from Ajax in July 2020, and he has represented the Blues on 83 occasions, contributing 14 goals and 10 assists in the process.
Last term, Ziyech featured made 44 appearances for Thomas Tuchel's side, scoring eight times and providing six assists, but he has largely struggled to show his best form since arriving at Stamford Bridge.
There has been speculation surrounding the Morocco international's future in recent months, with AC Milan believed to be keen to bring him to Italy for the new season.
However, according to transfer insider Dean Jones, Man United boss Erik ten Hag is also eyeing a reunion with the player that he managed at Ajax.
"The Ziyech move to AC Milan has stuttered a little and if that situation drags on let's not rule out the idea that Ten Hag looks to take him to United instead," Jones told GIVEMESPORT.
Ahead of moving to Chelsea, the attacker featured on 164 occasions for Ajax, scoring 49 goals and registering 80 assists during an impressive spell.
The Moroccan has won the Champions League, UEFA Super Cup and Club World Cup during his time with the Blues, while he lifted the Eredivisie title and KNVB Cup during his time in Amsterdam.
Ziyech still has another three years left to run on his contract with Chelsea, having penned a five-year deal upon his arrival in July 2020.
Man United are currently short of attacking options, with Paul Pogba, Jesse Lingard, Juan Mata and Edinson Cavani leaving on free transfers this summer.
The 20-time English champions are believed to be on the verge of signing Christian Eriksen on a free transfer, but a possible deal for Ajax's Antony has allegedly stalled due to the Brazilian's asking price.
Anthony Martial is back at the club this summer after an unsuccessful loan spell at Sevilla, and the Frenchman is now expected to remain at Old Trafford, having impressed in the early stages of pre-season.
Mason Greenwood remains suspended by the Red Devils, but Marcus Rashford, Jadon Sancho and Anthony Elanga are all options for the wide positions at the club.
There remains speculation surrounding the future of Cristiano Ronaldo, but it is believed that the Portugal international could stay at the club this summer due to a lack of suitors.
Ronaldo is not with the Man United squad in Australia due to a family issue, which remains private, and it is still unclear when he could join up with his teammates.