Striker Gallagher has impressed at Ewood Park after joining the club on a season-long loan in August despite the club's struggles at the wrong end of the Championship table.
Sam Gallagher impressing on loan at Blackburn Rovers
Gallagher has scored seven goals and assisted one goal in 17 games in the Championship for Owen Coyle's men and his performances for Rovers have alerted a number of their rivals.
Coyle has admitted he would love to make Gallagher's loan deal a permanent move, but they could now face a battle from other clubs higher up in the Championship and Premier League as a result of his eye-catching displays at Ewood Park.
Blackburn Rovers Sam Gallagher celebrates scoring with Scott Wharton
Several sides are understood to have made enquiries about signing him on loan or on a permanent deal when the transfer window reopens in January.
Gallagher is highly-regarded at Southampton after breaking into the first-team in the 2013/14 season under Mauricio Pochettino, making 20 appearances and scoring two goals.
Blackburn Rovers' Sam Gallagher celebrates another goal
However, Gallagher did not figure under Ronald Koeman in the last two seasons, with injuries preventing him from making an impression in the first-team.
Southampton have monitored Gallagher's progress at Blackburn and they could either call him back in January and include in him the first-team fold or send him out on loan again or they could decide to sell the former Plymouth youngster if their asking price is met.
Sam Gallagher of Blackburn Rovers in action with Richard Keogh of Derby County