Liverpool have been on the market for a new defender throughout the summer, with Southampton’s Virgil van Dijk the No 1 target.
Van Dijk has handed in a transfer request at St Mary’s but Saints say he will not be sold before the transfer window shuts a week today.
But Allardyce does not think they need the Dutchman and in Mamadou Sakho they have a player who can help out their leaky defence.
Sakho fell out with manager Jurgen Klopp in pre-season 2016 and was made to play for the Under-23s for the first half of the 2016/17 campaign.
He joined Crystal Palace on loan in January where Allardyce was in charge and excelled at Selhurst Park until suffering a knee injury.
Sakho’s ability with the ball at his feet has been questioned since he arrived at Anfield from Paris Saint-Germain in 2013 but Allardyce says that should not be the main priority for a defender.
“It’s easy for him (Sakho) to give it to players like (Philippe) Coutinho and people like that and let them get on with it,” he said on talkSPORT.
“For me, there is a big misconception, even in the Premier League, of the amount of ability that a centre-half has to have on the ball.
“He has to have a lot of ability but at the end of the day has job is defending and keeping clean sheets.
“Your first job is defending, get the ball and keep it simple.
“It’s very effective and Mama is very effective because he can get it down and play simple, play it into midfield.”
Liverpool have collected four points from their opening two Premier League games of the season and play host to Arsene Wenger’s Arsenal at Anfield on Sunday (4pm) looking for a fourth win in a row in all competitions.