Roman Abramovich will strongly support his manager in the next window, with the Russian owner confident Tuchel can mount a serious challenge at Manchester City.
But plans for Gallagher, who will return from a season-long loan to Crystal Palace this summer, cast doubt on the moves of other midfield reinforcements, including Declan Rice.
Tuchel has been hugely impressed with Gallagher, who has been one of the stars of the Premier League season at Selhurst Park.
It has convinced him that the player is ready to compete for a regular first-team role on his return to Stamford Bridge, which will add more depth to an already well-stacked midfield department.
Chelsea have long been interested in Rice, who will be one of the most sought after players in the Premier League at the end of the season. Manchester United are among clubs set to test West Ham’s resolve to retain their most prized asset.
Monaco’s Aurelien Tchouameni has also been widely watched by Chelsea scouts this season and could still be Rice’s preferred option – particularly if West Ham rule their player out of a move.
But while Chelsea are actively considering this pair, there is also recognition of the strength they already have in midfield in the form of N’Golo Kante, Jorginho and Mateo Kovacic ahead of Gallagher’s imminent return.
On loan, Saul Niguez is set to return to Atletico Madrid, while the futures of Ruben Loftus-Cheek and Ross Barkley hinge on what offers Chelsea receive for the pair.
Rice or Tchouameni would block Gallagher’s progress, meaning Tuchel will have to think carefully before pursuing his interest.
The situation would change if any of Kante, Jorginho or Kovacic left this summer – but there is no indication that any of them are looking to leave.
Chelsea face Palace on Saturday with Gallagher unavailable as Premier League rules prohibit him from playing against his parent club.
It will be a major loss for Patrick Vieira, who made the 22-year-old a key part of his team.
Gallagher has scored seven goals in 24 appearances for Palace, all in the league.
He impressed while on loan at West Brom last season and was in Tuchel’s plans this term, until the opportunity to develop his game further under Vieira arose.