Rodrigo, who has yet to report for the club's latest pre-season camp, is reportedly one of a number of Valencia stars to have been told that they will be sold this summer, due to the perilous financial position the club currently finds itself in amid the coronavirus crisis.
Former club captain Dani Parejo and fellow midfielder Francis Coquelin have already been moved on for cut-price fees, and another prized asset looks set to follow suit in the coming days.
Rodrigo moved to Mestalla from Benfica for €30 million (£27m/$35m) in the summer of 2015, and has since scored 59 goals in 220 appearances for Valencia.
The Spain international played a key role in Valencia's run to a fourth-place finish in La Liga in 2018-19, but they only finished ninth last term.
Barcelona were heavily linked with Rodrigo in January, having been desperate to bring in an extra striker to fill in for Luis Suarez, who was sidelined with a serious knee injury at the start of the year.
The Blaugrana were ultimately unable to agree on a fee with Valencia , who were holding out for €60m (£51m/$66m) for a prized asset.
Valencia are likely to accept a far lower offer for Rodrigo this time around, as they seek to pay off a sizeable debt by overhauling the squad during the summer window.
Leeds will offer a fee in the region of €30m plus add-ons, as Marcelo Bielsa continues to prepare for the club's long-awaited return to the Premier League.
The Whites stormed to the Championship crown to gain promotion to the top flight after a 16-year absence, and have already signed five players ahead of the new season.
Helder Costa, Illan Meslier, Joe Gelhardt, and Cody Drameh have arrived at Elland Road on permanent deals, while Manchester City winger Jack Harrison has returned to the club on loan.
Leeds were also linked with former Paris Saint-Germain striker Edinson Cavani , who is currently available as a free agent, but Rodrigo could become Bielsa's sixth signing of the summer.
Rodrigo is keen to decide on his own future as he wants to ensure that, if he does move, he goes to a club where he will play regularly ahead of next summer's rearranged European Championship. He is also aware that it is likely to be the last major contract of his career.