West Ham have asked to be kept informed on Marcus Rashford’s situation, talkSPORT understands.
Rashford faces an uncertain future at Manchester United having recently been dropped by head coach Ruben Amorim.
The 27-year-old has admitted he is ‘ready for a new challenge’ away from Old Trafford, with United open to offers.
West Ham would consider a loan move for Rashford but know he is more likely to join a top European side.
Napoli, Juventus, AC Milan and Borussia Dortmund have all been credited with an interest in the England forward.
It is understood the Red Devils are resigned to the fact they cannot sell Rashford this month and a loan deal is their only option.
The news coincides with the Hammers appointing Graham Potter as their new manager on Thursday morning.
Julen Lopetegui was sacked on Wednesday after a dismal eight months in charge and left West Ham 14th in the Premier League.
Former Chelsea and Brighton boss Potter has signed a two-and-a-half year contract at the London Stadium.
“Very excited, very proud day to be head coach of this amazing club,” he said in his debut press conference.
“It’s a big tradition, big history, big expectation. A big challenge. It’s a bit like Christmas for the adults.
“Excited, not the best of sleeps last night just from excitement. Really looking forward to meeting the players, meeting our supporters and getting going.”
Rashford may become the latest player to swap United for West Ham after Aaron Wan-Bissaka completed a move last summer.
The right-back has impressed in his first season at the club having started in 18 of his 20 Premier League appearances so far.
Jesse Lingard enjoyed a strong spell in east London when he signed on loan from United for the second half of the 2020/21 season.
He netted nine goals and assisted another four in 16 outings but, despite being linked with a permanent switch, he left in the following summer.
Rashford is thought to be the highest earner at United on more than £300,000-a-week.
The forward has scored seven goals in 24 appearances this season but hasn’t played in the Premier League since December 7.
Amorim omitted Rashford from his squad for four consecutive league matches before naming him on the bench in their 2-0 home defeat to Newcastle.
He also missed the 2-2 draw against rivals Liverpool on Sunday but this was due to illness.