The Uruguayan scored 19 goals in 59 appearances for Manchester United, before leaving the club this summer following the expiration of his contract.
Cavani has attracted interest from the likes of Villarreal and Boca Juniors, while he was reportedly turned down an offer to join Nice.
According to Goal, the 35-year-old is expected to sign a two-year contract with Valencia where he will to earn €2m (£1.7m) a year.
A move to Valencia would result in Cavani featuring in four out of Europe's five top leagues, having previously played in Italy, France and England.
Meanwhile, Everton are reportedly considering a move for Newcastle United winger Miguel Almiron.
With the transfer window set to close next week, Frank Lampard is keen to make further additions to his squad, with strengthening in attacking areas a priority.
According to The Sun, Everton are interested in signing Almiron from Newcastle, although the report suggests that they are yet to make an offer for the 27-year-old.
Almiron has only scored 15 goals and contributed five assists in 126 appearances for the Magpies, but he has started all three league games this season and found the net in Newcastle's 3-3 draw against Manchester City on Sunday.
However, the Magpies are open to selling the Paraguay international, who joined the club two years ago for a £20m fee.
Fulham are reportedly targeting Paris Saint-Germain left-back Layvin Kurzawa.
The Premier League club have made seven additions to their side over the summer, including Issa Diop, Kevin Mbabu, and Shane Duffy who have all strengthened the backline.
However, Fulham are looking to sign another defender with Italian football journalist Fabrizio Romano reporting that they are interested in Kurzawa.
The 29-year-old, who has two years left on his contract, has been deemed surplus to requirements at PSG after making one appearance for the club last season.
Marco Silva is keen to bring the 29-year-old to the Premier League, with Fulham regarding Kurzawa as one of their top targets before the transfer window closes.
Elsewhere, Roma are reportedly edging closer to signing former Torino striker Andrea Belotti.
The Italian scored 113 goals in 251 appearances for Torino before leaving the club at the end of last season once his contract expired.
Belotti has had to be patient in his search for a new side, however he looks to have found a destination as according to Calcio Mercato, he is set to sign for Roma.
The Europa Conference League winners are expected to sell Felix Afena-Gyan to Cremonese for €7m (£5.9m), which will give Roma additional finances to sign Belotti on a three-year contract.
Belotti is set to sign a deal that would earn him €2.8m (£2.4m) a season and the striker is expected to arrive in the Italian capital in the next few days.