Manchester United have chosen their favoured David de Gea replacement
De Gea is out of contract in summer 2020 and has yet to put pen to paper on a new deal.
PSG and Juventus have been linked with the Spaniard in recent months, and United may opt to sell if the goalkeeper continues to stall on a new contract.
The club hope that De Gea will eventually decide to extend his stay at Old Trafford, but they have identified Cillessen as their leading target if the ex-Atletico Madrid man moves on.
The Dutchman is second choice at Barcelona behind Marc Andre ter Stegen and will push for a move away this summer.
The Blaugrana are reportedly willing to accept offers of around £22m for Cillessen, who moved to Catalonia from Ajax in 2016.