The forward, who impressed at the recent World Cup in Qatar with the Netherlands, is currently on loan from Burnley at Besiktas.
Reports suggest that United have agreed a deal with Burnley for the 30-year-old to take him on loan for the remainder of the season, but are now awaiting news from any conversations between the Championship club and the Turkish side.
Weghorst has scored nine goals in 19 games for Besiktas, who want to finalise their own replacement before agreeing to let him go early.
The Dutchman has informed the Istanbul club that the opportunity "is too good to turn down" at this point in his career, and there is hope on all sides that a deal will be done before the window closes.
Insiders have also suggested Besiktas were hoping to make the loan deal permanent and may look for some form of financial compensation.
On Monday afternoon, Besiktas released a club statement belittling the "fictitious" reports of a possible €2.5 break clause fee.
"After the match of our Football A Team against Kasimpasa in the Super League, there was a need to make a statement due to speculative news in the media about our football player Wout Weghorst.
"The claim that there is an exit clause in our football player's contract, stating that his contract can be terminated with compensation of €2.5 million in case of an offer from the Premier League, is fictitious.
"However, the news that the player in question will leave the team on Tuesday is completely untrue. The initiative regarding Wout Weghorst belongs entirely to Besiktas Gymnastics Club."
"We also state that if there is a development on this issue, our esteemed community and the public will be informed."
Erik ten Hag's side are being linked with a host of other striker options, including Atletico Madrid's Joao Felix and Cameroonian star Vincent Aboubakar.
The latter is available on a free transfer after leaving Saudi side Al-Nassr as the club made room for the arrival of Cristiano Ronaldo, while a move for Felix is unlikely given the financial restrictions in place at Old Trafford, with the Glazers still looking to sell the club.
