However, Poulsen will take some convincing after expressing reservations about such a deal and a willingness to stay and fight for his place in Turin.
Poulsen moved to Juventus from Sevilla last year in a deal worth £9 million but the 28-year-old has struggled to settle, hampered for much of his time in Italy by injury.
Portsmouth manager Tony Adams see Poulsen as the perfect replacement for Lassana Diarra, who joined Real Madrid at the start of the current transfer window, according to a report in the Independent.
Speaking to a Danish newspaper, Poulsen said: 'I am completely focused on getting enough playing time [at Juventus].'
The player's agent, Joern Bonnesen, however, was much more forthright. 'Christian has no intention of leaving Turin,' he said.
Poulsen has played 60 times for his country and, despite his reticence over a transfer, Portsmouth will step up their attempts to change his mind after coming up short in their search for much needed midfield reinforcements.
The club have already seen a £4.5 million bid for former player Gary O'Neil rejected by Middlesbrough, despite the player's desire to return to the south coast having failed to settle in the north east.
Portsmouth had better news in their dealings with Liverpool over Jermaine Pennant, after a loan deal was secured until the end of the season.
Portsmouth had hoped to sign the winger on a permanent arrangement but with Pennant's contract at Anfield due to expire in the summer he wanted to keep his options open.
An inquiry was made over the availability of Adams' former Arsenal team-mate Patrick Vieira but the Portsmouth manager has played down the possibility of bringing the Frenchman to Fratton Park after his interest cooled on learning of an injury to the Inter Milan midfielder.
'Patrick is someone we would be very keen to bring here,' said Portsmouth's chairman Peter Storrie.
'Obviously he is well known to Tony but my understanding is he has got an injury and that won't be possible in this window.'