Allardyce - who wants three new signings in January - also added he will need to sell a midfielder before he could make any move for Sevilla star Steven N'Zonzi, who he worked with at Blackburn.
Allardyce is rumoured to have a longstanding interest in the player, having previously recommended him to former club Crystal Palace.
Despite an unbeaten run of seven matches that has pulled them clear of the relegation battle, Everton have scored only 24 league goals this season and have been searching for a striker to replace Romelu Lukaku.
The Guardian report that Everton will sign Tosun from Besiktas for £25 million in the January transfer window. We need more goals if we are to maintain our position, we've started to struggle to create chance in recent matches so it's still one of our major problems.
"We've got more penalties than anybody else in the Premier League, which has contributed to a few points".
"That won't always happen so we need to strengthen in our goalscoring areas and that's new players". Players already here, like Sandro (Ramirez), haven't picked up the pace of the Premier League.
Despite making two appearances for Germany's Under-21 side, Tosun opted to play for Turkey at global level and has eight goals from his 24 caps.
"For me, knowing him from that age and knowing him now, yes I would like him but with the amount of midfield players I have at the moment, I'd have to move some player out to bring a player like Steven in".