Paul Ince has also been chatting about the Tottenham Hotspur star.
The Burnley midfielder has spoken to Rangers about a potential move.
Michail Antonio is reportedly in line for a new contract at West Ham.
The Dutchman spent last season on loan at the Eredivisie club.
The Northern Irishman was appointed by the Scottish Premiership side on Friday.
Ibrox side Rangers are interested in signing Burnley midfielder Joey Barton in the summer transfer window.
Southampton boss Ronald Koeman has been linked with the Everton managerial job.
The Shamrock Rovers star is to take an indefinite break from football.
The centre-back claims that Ranieri's reputation as a 'Tinkerman' is no longer accurate, following Leicester City's surprise Premier League title win.
Brendan Rodgers is reportedly considering a move for Steven Gerrard.