Pompey administrator Andrew Andronikou is quoted as saying that the Trotters have expressed an interest in the one-time England international.
Owen Coyle's presence at the Reebok Stadium is believed to have triggered the rumours, as he took the striker to Burnley on loan last season during his time with the Clarets.
Portsmouth's financial troubles are also well-documented and it is claimed that they are looking to offload around £15million worth of talent this summer, with Nugent among those expected to be shipped out.
"We are hoping to speak to David's agent over the next two weeks to find out what his client wants to do," said Andronikou.
"I am told he is trying to stay in the Premier League and Bolton are interested.
"We are looking at £2.5m upwards - that would be a good fee. We are certainly not going to recoup what we have paid for him, while I would like to avoid paying his level of wages."
Coyle, though, has distanced himself from the Nugent speculation, claiming he has made no approach for the 25-year-old frontman.
"I haven't spoken to anyone about David," he told the Bolton News.
"Don't get me wrong, I think he's a really good player who I worked with very closely at Turf Moor. And I'm happy to get linked with good players.
"But I'm not looking to bring him to Bolton, and I certainly haven't made any offers for him, as Portsmouth seem to be suggesting."
While keen to play down the Nugent link, Coyle has admitted that he is keen to bolster his attacking unit over the coming weeks.
"It would be fair to say we need a bit more competition up front - maybe one or two more," he said.
"It's that time of the year where we are being mentioned with a lot of players.
"We've put a few calls out, but at the moment, it is still very quiet."