Barry joined Everton on a season-long loan on deadline day in August, with the Blues effectively taking on the final year of his City contract.
As he is a free agent in July City would not want a huge fee for the 32-year-old, though his wages in excess of £100,000 a week may have to be negotiated down.
Sky Sports News reporter Alan Irwin confirmed that Everton were working on at least one deal, citing a source from within the club, which will almost certainly be his former Sky colleague and Everton's director of communications Alan Myers.
Should Barry sign a permanent deal then that would of course free up space in the squad for another domestic loan deal, with the rules stating that only two are allowed at any one time.
Three names have been mentioned, the first is former Toffee Jack Rodwell, who has endured a miserable time at City since signing in the summer of 2012.
A lot of that has been down to his dodgy hamstrings and I have grave reservations about signing a player with such a horrendous injury record - I thought we did amazingly well to sell him in the first place.
If someone can guarantee his fitness then he would certainly slot into the squad nicely and would suit Martinez's style of play better than he did under Moyes, who never seemed sure about where to play him.
His fitness, though, cannot be guaranteed so I'm very wary on that one.
His City team-mate and fellow former Everton player Joleon Lescott has also been named, though that remains more of a Twitter rumour than anything at present.
Another name linked with a loan to Goodison Park is Tom Ince, and this rumour is believed to have legs.
The Blackpool man's tour of the UK, seemingly holding talks with every Premier League club in the bottom half of the table, has become something of a deadline day joke and he could seemingly sign for any one of 10 sides.
He also had talks with Everton and Swansea earlier this month, though nothing came of it.
The main sticking point seems to be that Blackpool want the forward to leave on a permanent deal to guarantee a fee while Ince is keen to leave on-loan until the end of the season, where he will then become a free agent.
Ince would certainly offer Everton some pace and creativity in attack but is relatively untested at the top level so would be something of a gamble.
It would also mean we would go into the second half of the season short of cover in midfield and - should Jonny Heitinga move to Fulham - in defence.
I guess all we can do is sit and wait. Though while you do that make sure you have your say in our deadline day open thread.