The British newspaper claims that Newcastle are ready to sell the striker at the right price in the summer transfer window.
The two clubs who want to recruit the Senegal international have not been named by The Chronicle.
According to a report in The Chronicle earlier this month, Newcastle have put a £10m price tag on the 30-year-old.
Besiktas are keen on recruiting the Senegal international striker, according to Turkish news outlet Aksam.com.tr.
However, Cisse himself seems to be enjoying himself at Newcastle and wants to remain at St. James’ Park for the foreseeable future, as the following post on social networking site Twitter suggests:
Im proud to be wearing the number 9 shirt and im looking forward to this season!— Papiss Demba Cisse (@CissePapiss) June 23, 2015
Should Newcastle United sell Papiss Cisse?
Cisse is one of the better players in the current Newcastle squad, and the club should not make a rash decision over his future.
The Senegalese scored 11 goals and created six chances in 22 Premier League appearances in the recently concluded 2014-15 campaign.
For Newcastle to break into the top 10 of the Premier League next season, Cisse needs to be part of the team.
If the Magpies want to sell Cisse, then they should do so only after they have a suitable replacement lined up.