Silva has signalled his intention to leave Manchester City at the end of his contract, which is set to expire on June 30.
Valencia are keen to re-sign the Spain midfielder 10 years after he left the club for the Etihad Stadium but negotiations are being hampered by the uncertainty surrounding the implications of COVID-19 for players out of contract this summer.
FIFA have suggested contracts due to end on June 30 should be extended until the season can be completed but there is concern among Premier League bosses that the guidance is not legally enforceable.
Sources have told ESPN that Silva, who turned 34 in January, will have to either agree to a short-term extension to stay with City or decide to leave on June 30.
Valencia, seventh in La Liga, have offered a three-year contract. David Beckham's MLS franchise Inter Miami and Italian champions Juventus have also been linked with the World Cup winner.
Silva, who has played more than 400 times for City, is keen to add the Champions League to his trophy haul of four Premier League titles, two FA Cups and five League Cups, and Pep Guardiola's side are well-placed once the competition resumes after beating Real Madrid 2-1 in their round-of-16 first leg clash at the Bernabeu in February.
However, there are also concerns that an injury suffered during the remaining games could jeopardise his next move.
City are keen for Silva to stay and complete the season but the decision is set to be left to the player and his representatives.
Meanwhile, Valencia have joined other top Spanish clubs in announcing a pay cut for players and coaches to help ease the financial impact caused by the pandemic.
A statement from the club on Monday said many of its non-playing staff would be able to receive their full salary during the period of inactivity following an agreement with the players.
Valencia did not give details of the pay cut agreements.