Poulsen, 30, played for Liverpool boss Roy Hodgson at FC Copenhagen 10 years ago and is thought to be keen on a move to Anfield after falling down the pecking order with the Bianconeri.
GEAR:Get the new Liverpool kits
And with Mascherano demanding to link up with former Reds manager Rafa Benitez at Inter Milan last week, Hodgson is reportedly stepping up his chase for the Dane, capped 77 times by his country, despite his agent Joern Bonnesen refusing to comment.
“I do not like comment on speculation," Bonnesen told Tuttosport.
"The player will be available to consider any concrete offers. Meanwhile he is remaining calm and continuing to work."
Speculation began to mount over the weekend after Poulsen was left out of Juve's 2-0 Europa League qualifying win over Shamrock Rovers on Thursday, fuelling rumours that a move to Anfield was on the cards.
But Juventus general director Giuseppe Marotta confirmed Liverpool's interest in Poulsen had nothing to do with the player's omission.
"Liverpool have shown interest in Poulsen. But the fact that he did not play in this game [against Shamrock] is only due to a technical decision," he said.
With Mascherano desperate to complete a £25 million move to Inter before the transfer window shuts later this month, Hodgson is also thought to be in the hunt for Standard Liege midfielder Steven Defour after sending a delegation to watch the £10 million-rated Belgian in action last week.
But Hodgson faces stiff competition for Defour from Manchester United boss Sir Alex Ferguson, a long-time admirer of the 22-year-old having written to the player to wish him a speedy recovery from injury last year.
By James Martini
