Cavani has been without a club since leaving United as a free agent in July, having scored 12 goals in 41 Premier League appearances during a two-year spell at Old Trafford.

The Uruguay international's 200 goals for PSG, meanwhile, make him their all-time top goalscorer, and he turned down a return to Ligue 1 after attracting interest from Nice earlier this month.

Nice president Jean-Pierre Rivere said Cavani's desire to move to Spain was the reason those transfer talks broke down, and the 35-year-old now appears close to getting his wish.   

Speaking ahead of Tuesday's (AEST) clash with Atletico Madrid in LaLiga, Gattuso said: "I am optimistic by nature, we are working, talking, I think we have possibilities. 

"[Valencia owner] Peter Lim is working hard, and I think we are going to sign Cavani because Lim, at the moment, believes a lot in this possibility.

"When you talk about Cavani, he is not a normal player, he has played for big clubs and at the highest level for a long time. He is 35 years old but has an incredible mentality, I am talking about the technical part, not money, that is not a problem, there are two different things. 

"The problem is that a lot of people talk in an operation and it's not easy to close it in two minutes.

"We are working on it for two or three weeks, but we are going to wait and I hope that it will close in a positive way for us. We have done everything to solve it and I hope that the signing will be closed.

"We are talking about a champion, a footballer who has played in teams of a high level, I am also excited that he comes here."

Los Che, who have taken three points from their first two league games this season, are also set to conclude another loan deal for Tottenham's Bryan Gil, who spent the second half of last campaign at the Mestalla.

Gattuso revealed his belief the deal will go through when Spurs bring in a replacement, adding the young playmaker was "99 per cent" likely to make the move.