The 26-year-old is reported to be taking a medical today ahead of a move to the University of Bolton Stadium.
Sheehan, who has two full international caps for Wales, played 55 games in all competition for Newport last season, including 120 minutes in the play-off final defeat to Morecambe.
He was also included alongside Ricardo Santos and Eoin Doyle in the PFA’s League Two team of the year, announced earlier this week.
Having started his career at Swansea City in the Premier League, he made one cup appearance before moving out on loan to Yeovil Town and then Newport in 2016.
He stayed with the Exiles for the next four seasons, playing 164 games and scoring 15 goals.
But for 13 games at Yeovil, the midfielder’s entire career has been spent at League Two level – but his stats for Newport this season suggest a player who could suit Ian Evatt’s playing style well.
According to Whoscored.com Sheehan finished the season with an 81 per cent pass success rate – the fourth highest in the division - with the most accurate long and short balls in the Newport squad of any outfield player.
He also registered four assists and three goals for Mike Flynn’s side.
Wanderers still hope to add another Welsh international to their ranks this season in Declan John, who is available on a free transfer from Swansea. They already have full international Lloyd Isgrove and both Gethin Jones and MJ Williams, who have both represented their country at Under-21s level.
Wanderers last week made Dapo Afiolayan their first permanent signing of the summer, bringing the winger back after a successful loan spell from West Ham to sign a three-year contract.
The club is making no comment on stories linking them with Sheehan.