Gary spearheaded the U.K. programme in a bid to find the perfect singers to star in his new musical The Band, about a fictional boy band and featuring Take That's biggest hits.
Ratings figures have been mediocre to date, but Gary is now said to be hoping to give them a much-needed boost by hosting a mini Take That reunion on the finale of the show.
Robbie, who left the band originally in 1995 before reuniting with them between 2009 and 2012, is said to have agreed to the gig, according to Britain's The Sun newspaper.
"Gary wanted to finish off Let It Shine with a bang and he thought a Take That reunion to close the show was the perfect way to achieve it," a source told the publication.
"The idea is that it would also set the stage nicely for the musical to follow. Robbie seems very keen to get on board, so things are looking good."
However, the band will still be a four-piece, as Gary is said to have opted against even asking former bandmate Jason Orange to rejoin the group for the performance, because he knew he would say no. Jason left the group in 2014, saying in a statement that he had decided to call time on his songwriting and performing career.
"Jason just isn’t interested now, he has his own life away from Take That.
“With him out of the picture, Gary is pouring his energy into making sure their reunion as a four-piece is a huge success and blows the audience away," added the source.