Damien Francis' days at Norwich appear numbered after he pulled out of a pre-season friendly as Portsmouth stepped up their interest.
BBC Sport understands Francis, 26, told boss Nigel Worthington he was not mentally right to play at Colchester.
Norwich want £2m for Francis and deny claims from his agent that Pompey have increased their initial £750,000 offer.
Agent Tony Finnegan said: "Damien withdrew after Portsmouth made a further expression of interest."
Francis has told Norwich he is not prepared to play Championship football following the Canaries' relegation from the Premiership.
Worthington has made provision for Francis' departure with signings designed to replace him, but the Canaries boss is determined not to let Francis go cheaply and will try and hold out for a fee close to their asking price.
Portsmouth may face competition for Francis' services from Charlton and West Ham.
Finnegan said: "Norwich want to get the best price for him and I can understand that. But Portsmouth have been very serious from the outset.
"The fact he did not play at Colchester suggests a deal may be close and I hope it will be concluded in the best interests of everyone."
Pompey chief executive Peter Storrie also denied the south coast club had made a new offer for Francis.
Storrie said: "There has been no new bid from us. We have asked Norwich, as what was the current situation.
"In other words it is just a polite enquiry. Before we buy any more players we have to shift a few the other way."
Portsmouth chairman Milan Mandaric has said he hopes to make two more signings before the weekend - although he would not be drawn on a name.
"But it could happen because we have a couple of targets that we could close on in the next two days before the weekend definitely," he told BBC Radio Sport.
"But its hard to say because things move rapidly back and forth so we will have to wait and see what happens."
Portsmouth have already signed seven players during the close season but they have yet to find a replacement for midfielder Steve Stone, who was released at the end of last term.