26-year-old Muriqi is a prolific goal scorer in Turkey’s Super Liga, having found the net 13 times in 25 appearances this season.
A tower at 1.94cm (6 ft 4 in), Muriqi is Lazio’s first choice to strengthen the attack, with Simone Inzaghi thinking ahead to next season and the Champions League.
Fenerbahce value Muriqi in the region of €20m and Lazio could face competition with other clubs interested.
The Kosovan recently spoke to the Turkish media about his future.
“I’m at the most important club in Turkey,” Muriqi said. “I have a three-year contract and don’t want to talk about the market.
“I’m fine here, but it’s up to the club and all in their hands.”
Knowing there will be stiff competition for Muriqi, Lazio are also considering 22-year-old Colombian, Luis Suarez, currently on loan at Real Zaragoza from Watford.
Vojvoda for the flanks
Lazio are also looking at cover for wide men Manuel Lazzari and Senad Lulic.
For the right side of midfield, they have another Kosovo international on their radar: Mergim Vojvoda of Standard Liege.
The Belgian club has set an asking price of €7m for 26-year-old, who has played in Turkey since 2014.