Begovic wants to leave Chelsea after struggling for game time at Stamford Bridge.
The Bosnia international has been forced to play second fiddle to Thibaut Courtois since joining from Stoke in 2015.
Bournemouth are frontrunners to secure his signature ahead of tomorrow's transfer deadline (11pm).
Eddie Howe remained coy when asked about Asmir Begovic
Bournemouth boss Eddie Howe wants to add to his squad
Chelsea transfers: Deadline day ins and outs rumours rated
Mon, January 30, 2017
Football Whispers have rated Sunderland's chances in the transfer market ahead of deadline day (1 – unlikely, 5 – likely)
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Football Whispers have rated the likelihood of Chelsea transfer deals (out of 5)
And Howe has refused to rule out a late move for the Blues' want away star.
"I never comment on individual targets from our perspective," the Cherries boss said.
"We've been active in the market, looking for players, but I wouldn't give you any clarity on a position.
Asmir Begovic has had to play second fiddle to Thibaut Courtois
"I'm not going to give you anything on [Begovic] I'm afraid. Sorry to disappoint you.
"This is the most difficult transfer window I've been involved in; the pool of players is so small.
"We have been looking, but we'll see what happens. Any player has to benefit the team."