Begovic, 28, has established himself as one of the top goalkeepers in the Premier League during his time with Stoke, but could now leave the club this summer.
The Bosnian international has just one year left on his contract at the Britannia Stadium, making him a target for rivals clubs in the process as they sense a potential bargain.
Last week, the Daily Mail reported that Aston Villa boss Tim Sherwood had lined up Begovic as a target as he bids to replace Brad Guzan in the Villa goal, but the latest reports cast doubt over the possibility of Begovic joining Sherwood's men.
That would involve being backup to Thibaut Courtois, and despite the possibility of Begovic barely playing under Jose Mourinho, Begovic is seemingly looking to make the move to Stamford Bridge.
Any hope for Aston Villa?
Given Begovic's reputation in the Premier League, it was always going to be ambitious for Aston Villa to target his signature this summer.
The lure of Chelsea is too much for many players to turn down, and despite Villa clearly offering better first-team opportunities, playing in the Champions League with Chelsea could seal the move in Mourinho's favour.
The lingering hope for Villa would be that Begovic would rather play at this stage in his career, yet despite that, their chances of signing the Stoke goalkeeper look bleak right now.