The 30-year-old is being tipped to sign a new two-year contract with the Red Devils despite being heavily linked with a move away from Manchester United this summer.
The Belgium international was set to become a free agent at the end of the month after failing to agree to a new contract with the Red Devils.
The defensive midfielder has been a useful player under Portuguese head coach Mourinho at Old Trafford.
However, Fellaini wants a significant upgrade on their £80,000 a week deal at Manchester United, which was proving problematic.
Arsenal had even been linked with a sensational swoop to sign the Belgium international from Manchester United this summer.
However, Belgian reporter Terreur has backed up recent reports that suggest Fellaini is set to sign a new two-year deal at Manchester United.
“Mourinho has always been keen to keep him,” Terreur told the Transfer Talk podcast.
“He has been telling Fellaini to sign that deal. His agent had one meeting with Arsenal.
“They never pushed for a deal.”
Manchester United signed Fellaini in a £27m deal from Premier League rivals Everton in the 2013 summer transfer window.
The Red Devils finished in second place in the Premier League table last season, while Manchester United lost 1-0 to Chelsea FC in the FA Cup final at Wembley last month.
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