Big Sam is set to seal a deal for Tal for next season and beyond after moving close to a pre-contract agreement with the 30-year-old Maccabi Haifa midfielder.
Allardyce told the club's website: "I am hopeful that a pre-contract deal will be concluded later this week.
"We are just awaiting the medical results and hopefully he will sign.
Allardyce continued: "He's a quality player, an attacking midfielder in the mould of Yossi Benayoun at West Ham and, if he can make the same impact on the Premiership that Benayoun and Tal Ben Haim have made, then we'll have a hell of a player.
"He already has Premiership experience with Everton so he should be a good acquisition."
Tal is delighted to get a second chance to make an impact on the Premiership.
"I was suprised by the (Bolton) offer," he told the Israeli media.
"I know it causes a lot of problems for Haifa next season but (coach) Roni Levi gave me his blessing."