First up is Aiden McGeady. The Spartak Moscow winger has long been linked with a move to Everton, even when David Moyes was in charge last season.
He cost the Russian club £9.5million in 2010 but is out of contract in the summer and so can open discussions with rival clubs from this month.
Everton could negotiate a cut-price deal with Spartak to sign the 27-year-old now, but the latest reports suggest Roberto Martinez is keen to sign him on a free transfer.
It is believed that the Toffees are close to agreeing a pre-contract agreement to sign the Republic of Ireland international upon the expiry of his contract at the end of the season.
Back on English shores and Blackpool forward Tom Ince is also believed to be on Martinez's wanted list. Ince was sold to Blackpool by Liverpool as a teenager in 2010 but has shown remarkable development since then and is now regarded as one of the Championship's brightest talents.
He was linked with a move away from the club last summer but rejected the chance to sign fro Cardiff and began the season at Bloomfield Road.
However, with his contract up at the end of the season Blackpool will be powerless to stop him leaving, though they would be due a compensation fee as he is under 21.
Reports suggest that Ince is set to meet Swansea boss Michael Laudrup and Roberto Martinez this week over a potential summer move.
A switch to Swansea would be surprising, given the reason he snubbed Cardiff was to remain in the north-west. That puts Everton at an advantage and could help swing negotiations their way.
A third player linked with the Blues is Dundee United defender Andrew Robertson. The 19-year-old only joined United in the summer from Scottish League Two side Queen's Park but has put in a number of impressive performances in the top flight so far this season.
Martinez travelled to Scotland to watch Robertson, seen as a long-term replacement for Leighton Baines, in action against Hibernian over the weekend.
United will be reluctant to let the defender go, but reports claim a bid in the region of £750,000 would be enough to do a deal.
Once player who may not be on the move is Johnny Heitinga. The Dutchman snubbed a move to West Ham earlier this month but has still been told he can leave in order to find first-team football.
Heitinga is out of contract at the end of the season so any fee would be minimal, indeed the West Ham deal would have seen them simply taking over the remained of his contract, saving Everton £1.5million in the process.
However, reports suggest Heitinga may well sit on his contract after all. The risk is that his lack of regular action could cost him a spot in the Netherlands World Cup squad. However, that would be negated by a lucrative move to a new club on a free transfer.
The ball is in Heitinga's court and I guess it depends on where his priorities lie.