Rodrigo is available as cash-strapped Valencia have placed their entire squad up for sale due to financial issues caused by the coronavirus pandemic.
The forward is valued around £30 million but the La Liga outfit may reduce their asking price if Leeds table a respectable offer, according to transfer expert Gianluca Di Marzio.
The 29-year-old has two years left on his current contract but his future lies elsewhere with Valencia's struggles.
Rodrigo came through Real Madrid's youth academy yet never made a senior appearance.
He signed for Bolton Wanderers then penned a deal at Benfica before sealing a switch to Valencia.
He scored seven goals in all competitions last season. He enjoyed his most prolific term in the 2017/18 season, bagging 19 goals in all competitions.
Leeds, meanwhile, have already signed French goalkeeper Illan Meslier, who spent time at the club last season, and Jack Harrison, who also played for them last term, on a loan deal.
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They're also keen on signing Brighton's Ben White who starred for Leeds last season.
Harry Wilson, Ryan Kent and Said Benrahma, among others, have been linked with a transfer to Elland Road, too.
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