Ander Herrera had a fine season for Manchester United, winning the club's Player of the Year award.
His performances have led to talk of a summer move to Barcelona to link up with former Athletic Bilbao boss Ernesto Valverde.
However, The Mirror claim they are not alone in wanting to sign the 27-year-old, with Valencia also lining up a £30million move for him.
The report says the Spanish club's manager Marcelino wants Herrera and has told owner Peter Lim to make the deal happen.
Ander Herrera is wanted by Valencia boss Marcelino
Jose Mourinho want Ander Herrera to sign a new Manchester United contract
Marcelino knows Herrera well having worked with him previously at Real Zaragoza.
He reportedly wants to build a team around the 27-year-old which is capable of challenging for the Champions League next summer.
However, The Mirror claim United have rebuffed Valencia's initial approach for Herrera, insisting he is not for sale.
The Spain international is under contract at Old Trafford until June 2018 and the Red Devils are keen to see him extend his stay.
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The Sun claim United are prepared to offer the midfielder a new four-year deal to ensure he stays put.
It is said Jose Mourinho wants to reward him for his fine displays by offering him a £180,000-a-week contract.
Herrera's current deal is worth £90,000, meaning he stands to double his wage.