Niasse has been used as Everton’s first choice striker of late, and Allardyce admits that the Senegalese international is now proving very hard to take out of his side.
Tosun has impressed in training in Dubai, with Everton going away for some warm weather training.
There had been some suggestions that Tosun would come back into Everton’s starting plans now.
However, Allardyce’s latest comments suggest that Niasse is going to continue up-front for the Toffees.
He said: “I think Oumar’s position at Everton has never been as good as it’s been at the moment. He’s got goals and assists to his name and he’s started games on a regular basis, and the competition with him, Dominic and Tosun is fierce.
“Oumar has grasped that position and the moment and it’s made it difficult for me to replace him at this moment in time.”
Tosun could now be left on the substitutes’ bench again, as Everton take on Watford tomorrow evening.
Tosun has played just 12 minutes over Everton's last three matches, with frustrations rising around Goodison Park over his consistent omissions.