The former Magpies striker believes the Senegal international should stay put despite the player reportedly wanting a move away from Sports Direct Arena
It appears contract talks between the Magpies and the 27-year-old have stalled, meaning the player could leave in January for £7 million - his current buy-out clause.
And Kluivert believes the goals he scored last season will have caught the interest of several clubs, especially if his good form continues.
|13/10||Demba Ba is 13/10 to score anytime against Norwich bet365
Kluivert told BBC Sport: "Stick with your club and, if you do well for another year, you can look to another club.
"[Ba] did a great job and scored a lot of great goals last year. It is very easy to say after he had a good year with Newcastle that he wants to leave.
"He's a great striker and I bet a lot of clubs want him and that's probably why [his agent] said that."
Kluivert also called on Magpies manager Alan Pardew to make Ba feel wanted on Tyneside, after the Senegal international was dropped to the bench for the Magpies' last Premier League clash at Everton.
He added: "I think [Pardew] knows another big club are after his player so for a manager at Newcastle, it's not an easy job.
"He has to convince the player that he is a very important for the team and not to say directly that he wants to leave.
"It's not a good thing for a manager to say that in public."