Liverpool's hopes of luring Paris Saint Germain defender Mamadou Sakho to Anfield have been given a boost after AC Milan vice president Adriano Galliani confirmed the club were not looking to sign a defender.

The France defender could be poised to leave the Ligue 1 champions having fallen behind the Brazilian duo of Thiago Silva and Alex in the defensive pecking order with €32m summer signing Marquinhos also in the frame at Parc de Princes.

Sakho is desperate to secure consistent first team football this season to strengthen his chances of securing a place in France's World Cup squad next summer, something under threat if he continues to start games on the bench.

Liverpool have been persistently linked with the towering centre half as they seek to address their own defensive concerns with reports on Wednesday suggesting the club were ready to launch a formal offer.

Serie A giants Milan have also been closely linked with a move for Sakho, but the club have closed the door on a move for the centre half this summer with Allegri confirming they are concentrating on strengthening other areas of their team.

"Our coach has specifically asked for a centre forward. Not a second striker, nor a midfielder or defender," Allegri told Sky Sport Italia.

"If he'd had Giampaolo Pazzini (who is unavailable through injury) at his disposal, then he wouldn't have made that request."

Sakho, who made his debut for the Parisian giants as a 17-year-old, was an unused substitute for his club's opening two games of the new Ligue 1 campaign and was left out of the squad completely by manager Laurent Blanc in last weekend's win over Nantes.

Far from pleased with his increasingly peripheral role at the club, Sakho has contemplated his future throughout the summer, announcing that whatever decision he makes before the closure of the transfer window will be made with his international aspirations in mind.

"When you are an ambitious player, you dream all the time of wearing the colours of your country," Sakho told Le Parisien last month.

"This summer, I've made a clear choice, taking into account the French national team."

Liverpool's already thin options at centre half took a hit on Tuesday night when Kolo Toure pulled up in the club's 4-2 victory over Notts County in their Capital One Cup clash, with the Ivorian a major doubt for the visit of Manchester United on Sunday.

With Sebastien Coates ruled out for the rest of the season and Martin Skrtel only just returning to full fitness, Brendan Rodgers is left with just Daniel Agger and Andre Wisdom as his only fit centre halves, with the void left by Jamie Carragher's retirement still gaping.