Roman Abramovich will back his manager heavily in the next window, with the Russian owner convinced that Tuchel can mount a serious challenge to Manchester City.
But the plans for Gallagher, who will return from a season-long loan at Crystal Palace this summer, place doubt over moves for other midfield reinforcements – including Declan Rice.
Tuchel has been hugely impressed with Gallagher, who has been one of the breakout stars of the Premier League season at Selhurst Park.
That has convinced him that the player is ready to compete for a regular first-team role when he returns to Stamford Bridge, which will add more depth to an already well-stacked midfield department.
Chelsea have long-standing interest 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 the clubs ready to test West Ham’s determination to keep hold of their most-prized asset.
Monaco’s Aurelien Tchouameni has also been extensively watched by Chelsea scouts this season and could yet be the preferred option to Rice – particularly if West Ham price their player out of a move.
But while Chelsea are actively considering that pair, there is also an acknowledgement of the strength they already have in midfield in the form of N’Golo Kante, Jorginho and Mateo Kovacic before Gallagher’s impending return.
On-loan Saul Niguez is expected to return to Atletico Madrid, while the futures of Ruben Loftus-Cheek and Ross Barkley are dependent on what offers Chelsea receive for the pair.
Rice or Tchouameni would block Gallagher’s progress, meaning Tuchel will have to think carefully about pressing ahead with his interest.
The situation would change if one of Kante, Jorginho or Kovacic move on in the summer – but there has been little indication of any of them looking to leave.
Chelsea face Palace on Saturday, with Gallagher not available because Premier League rules prohibit him from playing against his parent club.
That will be a major loss to Patrick Vieira, who has made the 22-year-old a key part of his team.
Gallagher has scored seven goals in 24 appearances for Palace, with all of them coming in the league.
He impressed while on loan at West Brom last season and was in Tuchel’s plans this term, until the chance to further develop his game under Vieira emerged.