Everton boss Roberto Martinez has stressed he has had no contact from Arsenal regarding Republic of Ireland midfielder James McCarthy and that he looks forward to seeing the player stay with the Toffees "for a long, long time".

Fresh stories linking McCarthy with a move away from Goodison Park have emerged over the last few days, this time with the Gunners said to be interested in signing him in January.

Additionally, it has been suggested Everton are trying to tie the 24-year-old, who they recruited from Wigan for €15 million on a “long-term deal” in September 2013, to a new contract in a bid to ward off the interest.

But when asked about such talk at his press conference to preview Wednesday’s Premier League home clash with Hull, Martinez emphasised Arsenal had not been in touch.

And the Spaniard added: “James is someone we rate very highly, otherwise you wouldn’t have seen the sort of investment we made on him.

“We are delighted with his form and I’ve always believed he is a typical Everton player, can grow and can get better. He has a long-term contract and it was a huge investment.

“I always enjoy seeing good reports on our players, and I see the potential interest or the good compliments that can be paid towards James from the outside. But he is a player we look forward to seeing in the Everton top for a long, long time.”

McCarthy has been out of action nursing a hamstring problem, as has Toffees forward Steven Naismith, and both will undergo late fitness tests prior to Wednesday's match.

Martinez rates Naismith as having an “outside chance” of featuring, but is expecting the game will come too soon for McCarthy.

Of McCarthy, Martinez said: “He has showed good signs and we will continue to keep an eye on him.

“I think we need to get deep to the bottom of the problem, because it has been a little bit of a recurring one.

“It is just to do with the amount of games he has had to play.

“I think we could find the perfect formula for him to have the right training exposure and being able to cope with all the games. It is something we want to eradicate.”

Midfielder Darron Gibson (knee) will not be involved and it remains to be seen whether defender Bryan Oviedo and forward Arouna Kone might after both played and scored in an under-21s fixture on Monday as they continued to work towards match fitness.

Kone also joined Everton from Martinez’s old club Wigan in the same summer as McCarthy, but has made just six first-team appearances since due a knee injury, his last run-out coming in October 2013.

Martinez said of the 31-year-old Ivory Coast frontman: “We’ll have to be a little bit patient, but he looked really strong yesterday.

“It has been really frustrating as a new player coming into an exciting new club, because he hasn’t been able to show what he can do. You can imagine that frustration really affects you – he is desperate to show what he can do.

“But the fans have been really good with the amount of messages we have received. He feels the right moment is coming and it is going to be a very emotional time for him once he can show what he can do to every Evertonian.”

Mid-table Everton are set to face a former striker on Wednesday in Nikica Jelavic, who switched to Hull – currently struggling towards the bottom of the league, with no win in six games and defeats in each of their last four – in January.

“Coming back to Goodison will be a really good moment for him,” said Martinez, whose side were unbeaten in eight matches in all competitions before Sunday’s loss at Tottenham.

“We as a club always have a strong affection towards Niki and his career, and we wish him the best of luck – apart from tomorrow.”