Nkunku, 24, was on target against Rangers on Thursday night, but couldn't helped his side reach the Europa League final later this month in Seville.
According to BILD Sport, the France international 'would like to take the next step' at the end of the current campaign, when his contract is set to expire.
There have been no formal offers for the attacking midfielder as of yet, but Nkunku continues to be linked with a free transfer to Manchester United.
AC Milan and Bayern Munich are also interested in his services according to The Sun, with Paris Saint-Germain since joining the race for his signature.
Leipzig wish to tie their highly-rated Frenchman to a new improved contract this summer to fend off interest, which would mean the player stays for another year, earning £130,000-a-week, according to BILD.
United may then have to wait another season to land Nkunku, and pay a release clause in the region of £55million.
Nkunku has found the net a staggering 32 times and clocked up 20 assists in 49 appearances across all competitions so far this season.
It is clear to see why he is one of European football's highly-rated stars and has several clubs circling. He is also staring on the international stage with France.
Leipzig lost an exciting battle at a raucous Ibrox, despite Nkunku's glowing performance for the German side.
James Tavernier and Glen Kamara put Rangers two goals ahead on the night inside 25 minutes, before Nkunku fired past Allan McGregor.
Midfielder John Lundstram later settled the Ibrox nerves slotting past goalkeeper Peter Gulacsi on 80 minutes to send the Scottish giants to Seville on May 18.
For Leipzig, they host Augsburg on Sunday, with two games left to play in the Bundesliga.