Fans' favourite Gomes asked for a transfer shortly after PSV claimed their 21st league title last season, citing differences with managing director Jan Reker.
That has alerted Spurs with Reker admitting the London club have been in touch regarding the goalkeeper.
"Tottenham have informed us of their interest," Reker said in the Eindhovens Dagblad newspaper.
Although Reker insisted a deal has yet to be struck, he hinted it was close after revealing the club have already drawn up a list of replacements.
"It is true that Andreas Isaksson is one of the candidates to replace Gomes, but we are looking at other keepers too," he added.