Since his arrival at the Tottenham Hotspur Stadium, head coach Ange Postecoglou has given Spurs' midfield a fresh look with the partnership of Pape Matar Sarr and Yves Bissouma.
Furthermore, Rodrigo Bentancur has been used on a regular basis, with Pierre-Emile Hojbjerg and Oliver Skipp generally providing strength in depth.
However, despite Spurs' relative improvement during 2023-24, that has not prevented the North Londoners from being constantly linked with Gallagher.
The England international is regarded as a key man by Mauricio Pochettino, as shown by 34 starts and four substitute appearances being made in all competitions.
Gallagher is also third-choice captain at Stamford Bridge and is eager to pen fresh terms at his boyhood club having been required to spend numerous loans elsewhere before getting his chance in the senior ranks.
Nevertheless, it has been well documented that co-owners Todd Boehly and Clearlake Capital are prepared to cash in on the 24-year-old if it means significantly boosting the club's position with the Premier League's Profit and Sustainability regulations.
There have also been conflicting reports over any contractual negotiations, it being alleged that the relevant parties are no closer to an agreement with one claim indicating that Gallagher's demands were out of Chelsea's reach.
In the background, though, Football Insider says that Spurs are preparing to test Chelsea's resolve over their asking price with a lowball offer.
Spurs will allegedly propose a deal in the region of £30m, aware that Chelsea have a need to bolster their books before the final accounting date for 2023-24 on June 30.
Although it is suggested that Spurs would be prepared to go as high as £40m, it is still below the valuation that Chelsea have for the academy graduate.
The situation is complicated with Chelsea having been unable to attract suitable bids for other homegrown talent, such as Trevoh Chalobah and Armando Broja, and Boehly and Clearlake Capital face the prospect of constantly assessing whether there are other routes to generate the funds required.
From Gallagher's perspective, it is unclear whether he would be prepared to rush an exit from Chelsea, the player in a position where staying put this summer would theoretically result in Boehly and Clearlake being more determined to reach an agreement over a new contract.