Sam Allardyce will ask every member of Everton’s first-team squad whether they wish to be part of the club’s future before finalising transfer plans for January.

Allardyce hopes to sign a proven goalscorer when the transfer window reopens after the club failed to replace Romelu Lukaku in the summer. Allardyce admits his first signing “has to be correct for Everton and for my future here – make bad signings and you get the sack, it’s that simple”. But with 31 players in the first-team pool when fit, the 63-year-old is prepared to sell assets who consider themselves surplus to requirements. All will be asked directly in face-to-face meetings with the manager.

“If every player is honest enough when I finally get through the one-on-ones they will tell me if they want to stay or they don’t,” Allardyce said. “If you are going to be honest with the manager, or if they want to leave it a bit longer and see how it goes to January, then I’ll deal with it.

“I don’t want anyone here who doesn’t want to be here. By the same token there’s always a price to pay and the club accepts we are not going to be mugs and let people leave under value in today’s market. People might want to move because it hasn’t quite worked or they have not settled as well as they thought. Up until then all these guys have a chance.”

Davy Klaassen, the £23.6m signing from Ajax, and the former Málaga striker Sandro Ramírez both fall into that category having struggled to make an impact since arriving in the summer. But Allardyce insists every player has an opportunity to shape his transfer strategyover the coming weeks.

“At the moment we would look to add a goalscorer. Dominic [Calvert-Lewin] has done well, [Oumar] Niasse has scored a few. It is the hardest thing to recruit players who score goals and hopefully there is somebody that can be brought in. If not, we will have to try to get Sandro to contribute a bit more.

“When everybody is fit we have a 31-man squad. At this early stage adding more players to that would mean thinking ‘Who is going to come in for one of our players and am I prepared to sell them or rotate the squad a little bit?’ I don’t want to be in a desperate position in January. I want the players to show me that I don’t desperately need to sign anyone and that we are going to be OK for this season. Then it would be a key element of next pre-season. The hardest time of the year to recruit the players, and the most expensive time, is January.”

Allardyce, who hopes to appoint a psychologist at Everton in the next week, saw Yannick Bolasie return from a long-term knee injury on Monday as a substitute in the under-23s’ defeat by Leicester City. Jonjoe Kenny is close to signing a new contract that will tie him to the club until 2022. Dominic Calvert-Lewin could be next in line for a new deal.