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Fellaini is out of contract at the end of the season.
Fellaini, 30, is out of contract at the end of the season, but Mourinho is confident that a new deal will be agreed.
“The position is that we are almost there, but in football almost is not enough,” said Mourinho.
“I want to see the white paper with the United crest and (executive vice-chairman) Ed Woodward’s signature and Marouane’s signature.”
Fellaini has been much-criticised since arriving at Old Trafford from Everton in 2013.
However, he has been a favourite of Mourinho’s for his physical presence in the opposition box and the Portuguese coach hailed his impact off the bench after Romelu Lukaku limped off injured early in the second-half.
“We needed somebody who could give us something different to replace Lukaku’s height and power and aerial game. In the end we got the goal I think we deserved,” added Mourinho.
Discarded by Mourinho in a swap deal that brought Alexis Sanchez to Old Trafford, Henrikh Mkhitaryan cancelled out Paul Pogba’s early opener against his old club.
A much-changed Arsenal side were on course for their first point away from home in the league this year until Fellaini rose highest to flick home Ashley Young’s cross.
“For 70 minutes we were not bad, but we were a bit slow, slow-thinking, not really intense,” bemoaned Mourinho.
“But then after their goal, I reacted, the players reacted, the fans reacted, the intensity of the game improved.
“(The substitutions) gave width, gave us crosses, gave us set-pieces, but the crosses and set pieces needed a target.”
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