The 30-year-old goalkeeper is firmly behind Aaron Ramsdale in the pecking order at Arsenal and has made just eight appearances for the club this season.
He will have a year left on his contract at Arsenal in the summer and there are suggestions that he could move on before next season.
There are also claims that Arsenal have told Leno that he can leave at the end of the season and Bayer Leverkusen are interested in getting their hands on the German.
But according to Sky Deutschland, Leno and his camp have had no contact from the Bundesliga club thus far.
His representatives are not in touch with Leverkusen despite the rumours of their interest in the goalkeeper.
It has also been claimed that Arsenal have not delivered any ultimatum to Leno to leave the club in the summer.
However, he is likely to have options to move on from the Emirates at the end of the season and will consider all scenarios.
The German wants to play regular football and is not content at being the Arsenal number 2 for the moment.