Report: Hammers interest in Bournemouth keeper
The keeper is due to return from injury in the New Year. Derby, Birmingham and PSV Eindhoven are also said to monitoring the situation of Begovic, who is coming to the end of a loan spell at Azerbaijani club Qarabag.
The deal expires on December 31 and the Bosnia international is keen to join a new club, on either a temporary or permanent basis.
The Bosnian fell out of favour with Bournemouth boss Eddie Howe after a series of underwhelming displays for the Cherries.
Begovic signed from Chelsea for £10million in 2017.
He will find himself behind Aaron Ramsdale, Artur Boruc and Mark Travers upon his return to Bournemouth.
The 32-year-old still has two and a half years to run on his £60,000-per-week contract and any club taking him on loan would be expected to pick up a significant slice of his wages.