The Northern Ireland star is well known in Spain, after his hat-trick ensured a 3-2 victory over the national team in Belfast earlier this year.
Valencia sporting director Amedeo Carboni is thought to be an admirer since that performance, and he is sure the 27-year-old can provide competition for Fernando Morientes and David Villa at the Mestalla.
However, Dennis Wise may decide he wants to keep Healy but should Valencia make a significant cash bid, a sale may facilitate a much-needed strengthening of the squad.
"We received an offer from (Healy's) agent, but a striker is not what we need right now," said Carboni.