The Championship side are planning for a future without Said Benrahma, who is a target for Premier League teams.
The News says if they lose Benrahma, Brentford will go for Curtis from Pompey.
The Republic of Ireland international has been impressive this season, finishing as runner-up for the The News/Sports Mail's Player of the Season.
He has managed 14 goals for Pompey, putting him level at the top of the charts with John Marquis.
The winger has also contributed several assists to his teammates.
He does have a contract until 2023, but a big offer would be too hard for Pompey to turn down.