The veteran centre-forward is off contract at the end of next month and not expected to be offered new terms by Chelsea.
Lens' board are putting together a bumper summer transfer budget and would be confident covering Giroud's contract demands.
However for the moment, Fenerbahce are regarded as favourites to land Giroud with his former Arsenal teammate Mesut Ozil in regular contact.
The pair remain in touch and when with Arsenal, Giroud said of the German: "Mesut's game view is flawless and he plays very simple. We get along very well on the field. He is a very qualified football player."
Meanwhile, Giroud has seen his playing chances increasingly limited since manager Thomas Tuchel's appointment in January. So far this season, Giroud has taken the pitch in the Premier League 15 times, scoring four goals.
- updated May 12