Bolton Wanderers are reportedly keen on Leeds United manager Steve Evans.
Begovic briefly worked under Mourinho at Chelsea early on in the season.
Everton are reportedly interested in the Sevilla manager.
The 20-year-old midfielder's first start for Gareth Southgate's side saw him score twice as they recorded a 7-1 win in their second game of the Toulon Tournament.
Liverpool reached two cup finals this season, but Jurgen Klopp could get more time working with his players.
Mark Warburton has brought Joey Barton to Ibrox side Glasgow Rangers on a two-year contract.
The ex-Newcastle United boss has been out of work since leaving St. James' Park in March.
Ibrox will be Joey Barton's new home soon - and Burnley have thanked him ahead of his move to Rangers.
Jan Vertonghen has proved his worth to Tottenham Hotspur this season, forging a fantastic partnership with Toby Alderweireld at the heart of their defence.
The Northern Irishman secured a 12-month rolling contract with Celtic.