The Turkish giants are looking to replace Felipe Melo.
NTV.spor are claiming that the Brazilian is on his way out of the club and that the Liverpool man and Inter Milan star are the men being targeted to replace him. Gokhan Inler is also a potential target, but he is believed to want an Italian stay when he leaves Napoli this summer.
It was reported by The Daily Mail last month that Liverpool were ready to move the Brazilian international on this summer in order to make some money back after their busy summer so far.
Lucas has been a regular for Liverpool over the years but last term struggled to find his best form or fitness.
He played just 20 league games and was not in his best form when he did feature, but that does not appear to have put off Galatasaray.
Medel though is another option and he has recently been in terrific form for his national team. Currently at Inter Milan the former Cardiff man was one of the star players as Chile defeated Argentina in the Copa America this weekend.