Fellaini looks all-but set to end his five-year stint at Old Trafford and join a rival club when his contract expires at the end of the month.
But it is believed United are still keen to get the Belgium midfielder tied down to a new deal, with an offer remaining on the table to keep him.
Fellaini started just two Premier League games since the turn of the year and has been linked with a move away for some time.
Red Devils boss Jose Mourinho has expressed his desire to retain the services of the former Everton man, who moved from Goodison Park in 2013.
Speaking after Fellaini came off the bench to score a last-gasp winner against Arsenal in April, Mourinho said: “The position is that we are almost there but in football almost is not enough.
“I want to see the white paper with the United crest and Ed Woodward’s signature and Marouane’s signature.”
An unnamed top-six Premier League side is understood to have shown firm interest in signing the 30-year-old on a free transfer, with Fellaini now seemingly swayed by the offer of more regular football.
Meanwhile Diogo Dalot admitted he could not turn down the chance to join “the biggest club in the world” after completing his move to United from Porto.
The 19-year-old defender, who is understood to have cost in the region of £19million, has signed a five-year deal with a further 12-month option at Old Trafford.
He joins forces with compatriot Jose Mourinho, who rates the player as “the best full-back in Europe” in his age group.
Dalot told the club’s website: “Joining Manchester United is an unbelievable opportunity for me. I have grown up in Porto’s academy and I am so thankful for everything they have done for me.
But the chance of coming to the biggest club in the world is something I just couldn’t turn down. I’m excited about working with Jose Mourinho and learning everything I can from such a successful coach.
“I am looking forward to playing alongside the fantastic players in the squad.”
Dalot only made his Primeira Liga debut in February, but helped Portugal win the European Under-17s European Championships in 2016 and is a current under-21 international.
He told MUTV: “The European Championships was when I realised that I could do great things in football and, since then, I’ve been improving a lot and I hope to improve more.
“I know that this is one of the best clubs in the world and it is unbelievable to be here. I hope to achieve great things.”
Mourinho was delighted to get his hands on the Porto academy graduate, of whom he is expecting big things during his time at in England.
The manager said: “Diogo is an extremely talented young defender with all the qualities to quickly become a great player for this club.
“He has all the attributes that a full-back needs: physicality, tactical intelligence and technical quality, combined with a Porto academy mentality which prepares players for the maturity they need at the professional level.
“In his age group, he is the best full-back in Europe and we all believe he has a bright future ahead of him at Manchester United.”
Dalot is Mourinho’s first Portuguese signing for United, and the teenager is determined to repay the manager’s faith in him.
He said: “It’s very good. It was very important to make this choice and I hope to help him, because I know that he will help me to improve a lot.
“Age is not very important now in football. I think that if you work and you improve, I think you can handle it.”