When the Foxes were relegated from the Premier League in May, the expectation was that they would cash in on academy graduate, who had established himself as a key man.
However, the 25-year-old was instead kept at the King Power Stadium and has gone on to contribute nine goals and nine assists from 27 appearances in the Championship.
Enzo Maresca's side are in a position where they are expected to secure promotion back to the top flight, the advantage to third-placed Southampton being eight points.
With Dewsbury-Hall likely to be regarded as an integral part of the side should Leicester return to the Premier League, they remain in no rush to cash in on the 25-year-old.
Nevertheless, according to The Mirror, the decision has been made to place a £40m price-tag on the shoulders of the Englishman.
That is an attempt to ward off interest from several Premier League clubs who have been credited with an interest in recent days.
Arsenal have allegedly emerged as admirers at a time when Mikel Arteta is contemplating ways to strengthen his midfield, although any offer would likely come in the summer.
Brighton & Hove Albion may take a different approach with the Seagulls - who have money to spend - said to be in negotiations with their Leicester counterparts.
Roberto De Zerbi is eager to keep Brighton in the hunt for European qualification for the second season running, as well as win silverware with Brighton in the last 16 of the FA Cup and Europa League.
A report from Sky Sports News adds that Brentford also hold an interest, yet it is unclear whether Dewsbury-Hall would be prepared to depart for a club with no prospects of continental football for 2024-25.
He also has three-and-a-half years remaining on his contract, something that protects Leicester's position in the event that they miss out on promotion.
Leicester are on the brink of signing Inter Milan's Stefano Sensi, albeit remaining of the understanding that the deal will only go through if they free up space on their wage bill.