The report says Adrian is one name that has been mentioned in Liverpool circles though there has been no approach for the out-of-contract Spaniard, who is interesting Crystal Palace and Bournemouth among others.
The 32-year-old Hammer has already said his goodbyes to the supporters as he waved goodbye in his lap of honour following the 3-0 victory over Southampton and again at Watford on the final day of the season. Adrian joined West Ham in 2013 on a free transfer and made 150 appearances for the Hammers.
He has also been heavily linked to a return to Spain and in particular his former club Real Betis.