The La Liga giants lifted the trophy on home ground after a 2-1 victory over the Lions to complete their pre-season.
Galatasaray are however, already into their league campaign and returned to Turkey to prepare for their second league game of the season against Osmanlispor on Monday 24 August.
The Brazilian left-back has been closely linked with Chelsea and PSG over the summer.
The Daily Star reported that the Lions turned down a £5 million offer from Chelsea for the Brazilian full-back.
Galatasaray are understood to be holding out for at least £10 million for their star left-back.
Telles provided a total of two goals and three assists in 56 games for the Lions over the 2014-15 campaign and already has an assist this season.
The Brazilian joined the Lions on a £4.3 million move from Gremio in 2013 and still has another three-years left on his contract with the Istanbul giants.