The Lion’s have offered the Dinpro star a €1.9 million per season deal but they face fierce competition for the 25-year-old’s signature.
Konoplyanka has recently stated that he aims to play in the Premier League.
“My priority is to play in England. That’s where I want to continue my career and I will do that,” Konoplyanka was quoted as saying in the Express.
“Maybe clubs have met with Dnipro, but I can only say what I want to do.”
Stoke City are also reported to be interested in signing the Ukrainian international midfielder according to the BBC.
Konoplyanka reached the Europa League final with Dnipro last season but his side lost 3-2 against Sevilla.
Galatasaray finished last season as Süper Lig champions for the 20th time and booked a place in the Champions League group stages for the fourth consecutive season.
The Lions won the league and cup double for the sixth time last season and are currently managed by Hamza Hamzaoğlu.