The German's representative has admitted that he has already been contacted by several interested parties but insists that the Biancocelesti "have priority over all others"
The 35-year-old’s contract at Stadio Olimpico expires in the summer and with an extension yet to be agreed, the Germany international has been considering all of his options.
"With Lazio, both in the past and in this recent period, we have had several talks,” Klose's representative, Alexander Schutt, told Lazionews.eu.
“Currently there is still nothing signed. I do not deny that we are also in talks with other clubs, but Lazio will always have priority over all others."
Whilst there is uncertainty over Klose’s future at Lazio, team-mate Andre Dias has dismissed rumours that he is angling for a move away from the Italian capital.
"My family is happy in Rome," the 34-year-old told Lalaziosiamonoi.it. "It is not true that I'm waiting for proposals from Brazil or that I want to go to a another Italian club.
"I'd love to stay at Lazio and finish my career here as a player."