Arsene Wenger has admitted he does not want to kill Theo Walcott’s World Cup dream but claimed he cannot guarantee him sufficient game-time as Everton line up a £20million deal.

Toffees boss Sam Allardyce confirmed on Friday morning that Everton are keen on signing the 28-year-old and Standard Sport understands Southampton, West Ham, Newcastle and Valencia have all expressed an interest.

Everton and Southampton are furthest advanced in negotiations but Allardyce said: “I don't think there's a chance of a loan. It's not imminent but negotiations are going on.

"He's scored 100 goals for Arsenal from wide positions. His pace is a key strength which we lack. To add goals would be very important for me. And he's only 28.

"If it's possible to be over the line I'd be delighted. If that can be sorted out it would be a great addition from an attacking point of view.

"I don't get optimistic otherwise I get disappointed. I'll be very excited and enthused when someone, even if it's not Theo, has signed on the dotted line."

​Allardyce’s spoke just before Wenger held his pre-match press conference for Sunday’s game at Bournemouth and the Frenchman said: “I cannot tell you much more. Sam Allardyce has made that statement but Theo Walcott is here.”

Wenger confirmed that he has told Walcott he wants him to stay at Emirates Stadium but when asked by Standard Sport whether he had given him assurances over regular first-team football, the 68-year-old replied: “No, I cannot because you cannot just do it, it’s not honest.

“We will see, I have a good relationship with Theo and I don’t want him to be frustrated or lose an opportunity to go to the World Cup because Theo went to the World Cup in Germany in 2006 and we are now in 2018 and since he has not been for different reasons, so that is a sensitive subject.”

Everton are thought to be the only club capable of matching Walcott’s £140,000-a-week wage.

The 28-year-old is not agitating for a move but wants to play regularly in the second half of the season and is open to offers if Arsenal’s stance over game-time does not change.

A loan move would appear a suitable compromise but Arsenal have so far indicated Walcott, who has 18 months left on his existing contract, will either stay or be sold.

Arsenal have already sold Francis Coquelin to Valencia and will lower their wage bill further should Walcott depart but, in addition to scouring the market for a replacement should Alexis Sanchez leave, Wenger reiterated that the club are open to further business this month.

“We are open, we are on the market, we are active,” he said. “I don’t want to give you news that I can’t confirm after, though. In this transfer market, at the moment, it’s very difficult to come out with things as long as they are not signed because things can change very quickly.”

At the end of a series of questions about Sanchez and Walcott, one journalist thanked Wenger for his time. Wenger said in response: “Thank you very much… for torturing me!”