The Sun says United will offer Cavani a £2.5million rise to try and tempt him into staying for another year.
Cavani, 34, earns £200,000 a week but has yet to reveal if will leave this summer and return to South America.
United boss Ole Gunnar Solskjaer has held a couple of conversations with the Uruguay striker, yet the feeling was he would be off.
But the Red Devils have not given up and plan to offer him an extra £50,000 a week for another year's service.
The club do have an option of a further 12 months on the one-season deal he signed last summer, but it can only be triggered if Cavani also gives his approval.
The veteran hitman took a 35 per cent pay cut when he arrived at Old Trafford on a free transfer from Paris Saint-Germain — but landed a signing-on fee of around £6m.
Solskjaer remains hopeful an agreement can be reached over Cavani.