The 21-year-old has established himself as a regular at West Brom since joining on a season-long loan from Chelsea last summer, making 26 Premier League appearances.
Gallagher is set to return to Stamford Bridge at the end of the season, but could have the opportunity to head out on loan again next season.
Leeds, Newcastle and Crystal Palace are interested in acquiring the England Under-21 international’s services on a temporary basis in the summer.
However, the midfielder is determined to fight for a place under new Chelsea boss Tuchel when he returns to Stamford Bridge in the summer.
Gallagher’s determination to stay with the Blues could be a blow for Leeds, Newcastle and Crystal Palace, who are hopeful of signing him on loan.
The Premier League trio may need to work hard to try to change the player’s mind and tempt him to make the move in the summer.
Gallagher may find himself looking at limited game time under Tuchel at Chelsea and could rethink his stance.