National journalists Ben Jacobs (GiveMeSport) and Alex Crooks (talkSPORT) both state that the East Midlands outfit are about to make a move, with the Blues said to have already rejected offers from Premier Clubs this summer.
A £1.2m signing from Leeds in 2022, Davis played a key role in back-to-back promotions, registering 32 assists over those campaigns.
There was much talk of a potential England call-up going into last season, but the 25-year-old admitted he lost some confidence during the Blues' difficult Premier League relegation season.
Davis, who signed a new contract last October that runs until 2028, started last night's Championship opener at Birmingham City.
He is currently Ipswich's only fit left-back, with experienced back-up Conor Townsend having suffered an ACL injury in the final warm-up game of the summer.
Ipswich have already seen the likes of reliable defender Axel Tuanzebe (Burnley, free), influential skipper Sam Morsy (Kuwait SC) and top scorer Liam Delap (Chelsea, £30m) depart this transfer window, with £35m bids for England U21 star Omari Hutchinson, from Brentford and Nottingham Forest, having been knocked back.
Town boss Kieran McKenna has also confirmed that forward Nathan Broadhead 'wants to explore' a move to Wrexham, the clubs understood to have negotiated a £7.5m fee but Ipswich not willing to sanction an exit until reinforcements have arrived.
STU'S VERDICT
Will this turn Davis' head? Forest can offer European football and bigger wages, but there's no guarantee of starts there with Nico Williams having done so well in that role.
What is he worth in the current market? £20m+ would be my estimate. Regardless, Ipswich would be entitled to dig their heels in. With Townsend's injury, they really can't afford to let him go.
This summer, as chairman Mark Ashton outlined in June, was meant to be all about retention.