This is according to sources in Spain cited by talkSPORT, who report that the La Liga outfit - who have recently been taken over by the wealthy figure of Peter Lim - are poised to embark upon a £50 million spending spree, with both of those aforementioned Primeira Liga stars high on their list of targets.
Manchester United are expected to be in the market for a new central defender this summer, with the experienced duo of Rio Ferdinand and Nemanja Vidic both set to depart Old Trafford in the coming weeks.
Garay - who will go to the World Cup this summer and is generally viewed as the strongest member of a particularly weak Argentina defence under Alejandro Sabella - has been frequently linked with a move to Manchester United in recent months, with the 27-year-old having got his career firmly back on track at the Estadio da Luz following a disappointing stint in La Liga with Real Madrid.
Rodrigo, meanwhile, has also drawn plenty of positive plaudits for his performances this season, with the former Bolton loanee having played a big part in Benfica's extraordinary 2013/14 campaign.
An exciting attacking player, Liverpool's interest in taking the 23-year-old former Spanish youth international to Anfield appeared to be confirmed by eccentric Benfica boss Jorge Jesus last month following Benfica's Europa League clash with Tottenham.
Valencia finished sixth in La Liga last season, but it looks like the club could be about to become a major player in the transfer market following Lim's takeover at the Mestalla.