The midfielder is not in Ronald Koeman's plans this season.
Roberto Di Matteo needs to strengthen his midfield options if Aston Villa are to be successful this season.
The Everton midfielder has been impressed by the Blues youngsters in pre-season.
The Dutchman was named as the new Everton manager earlier this month.
Darron Gibson has penned a new two-year contract with Everton.
The 28-year-old was handed a new two-year contract by Everton on Thursday.
Republic of Ireland international midfielder Darron Gibson is out of contract at Everton at the end of this month.
Leon Osman, Steven Pienaar, Tony Hibbert and Darron Gibson are all out of contract at Everton this summer.
The Burnley midfielder is said to be in talks over a free transfer switch to Ibrox.
Everton were beaten 2-1 by Manchester United in the FA Cup semi-final yesterday.
The Republic of Ireland boss has suggested that Gibson should head out to the Championship.
Roberto Martinez addressed the media ahead of his side's trip to Chelsea in the Premier League.
Darron Gibson, Steven Pienaar, Aiden McGeady and Steven Naismith all face a fight to get into Roberto Martinez's first team this season.