The England midfielder has been in scintillating form this season and has scored three times and picked up four assists in 28 appearances across all competitions.
Rice is under contract with West Ham until 2024, but the Hammers are pushing for the 23-year-old player to commit his long-term future to the club.
The England international could make his exit in the summer if West Ham fail to secure a top-four place, with fifth-place Hammers one point adrift of fourth-place Manchester United.
The West Ham midfielder has been linked with United, Manchester City and Chelsea, with the Hammers demanding a hefty £100m fee to allow Rice to leave the club.
Parker has insisted that “without a shadow of a doubt” Rice could become club captain “within 12 months” of his arrival at Old Trafford.
The former United player added that the Red Devils could have a Premier League-winning midfield if they sign both Rice and Borussia Dortmund star Jude Bellingham.
Speaking to Kelbet, Parker said: “If you bring in Declan Rice, within 12 months, he’s your captain, without a shadow of a doubt.
“If you bring in those two [Rice and Bellingham] together, then you have a midfield of Premier League-winning types.
“When I watch him [Bellingham] play, I really like that. I like [the] fact that he doesn’t want to be type-casted to one position.
“He doesn’t want to be what all the young supporters call a ‘CDM’ as such. He wants to be called a midfield player, which I love. Because when you are a midfield player, that means you want to be all over the park.
“You are even happy to go into your own box, and more importantly getting near the opponents’ box and try to make and score goals. That’s what he can do. Doesn’t want his game limited.
“When you watch him play for Dortmund, his game is not limited.”
Harry Maguire is United’s current club captain, but his role as skipper has come under fierce criticism after his poor run of form.
United legend Rio Ferdinand believes the 28-year-old defender was handed the captain’s armband too early and named his preferred pick for the club’s skipper.
Featured Image Credit: PA
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