The Turk has signed a short-term contract until the end of the season.
Basturk, though, has barely played in the last 18 months for former club Stuttgart and, while that is a worry, Allardyce is hoping he has unearthed another hidden gem.
"If he can reproduce the form he has shown in Germany, then we're looking forward to him playing here," said Allardyce.
"The lad is committed. He wants to play in the Premier League, and we're going to give him the chance.
"I hope he is one of those gems I used to find at the old club down the road (Bolton) because he certainly has the quality and ability.
"What we've got is someone who has been cast off at the club he was at, and he wants to test his ability in the Premier League.
"I've had many of those so-called mercenaries in the past like Jay-Jay Okocha, Youri Djorkaeff, Fernando Hierro, Ivan Campo, Bruno N'Gotty, Stelios Giannakopoulos, and they've all been outstandingly good players in the Premier League.
"I hope this lad will do the same. He certainly has the pedigree anyway.
"We will introduce him in two to three weeks' time, and let's see what he can do."