Matteo Roggi wants a "big offer" for the Genoa goalkeeper this summer.
"I hope that Perin can play for a big club: he's had 120 appearances in Serie A and is the youngest goalkeeper to have had so much experience," he told Radio CRC, quoted by talkSPORT.
"If Genoa sell him they won't give him away, he'll only leave for a big offer."
If either Premier League club are really interested, it perhaps seems more plausible for it to be Liverpool, given that there is still something of a question mark over Simon Mignolet's capacity to be a reliable goalkeeper.
For the Hammers, Adrian has enjoyed a good season, while Darren Randolph has proven himself an able deputy in FA Cup action, with the Irons set to face Manchester United in a quarter-final replay at Upton Park.
With Perin's deal in date until 2019, Genoa have the upper hand in the negotiation process.