The 27-year-old big man is currently in rehab after suffering a torn Achilles while playing for the New Orleans Pelicans against the Houston Rockets in January.
Cousins had been expected to pen a lucrative multi-year max deal with the Pels before his potentially career-changing injury but has since been left in free agency limbo with lingering question marks over his health.
The Pelicans could yet table a huge offer for the talented superstar but after similar injuries impacted the production of the likes of Kobe Bryant and Wes Matthews in recent years, the franchise is likely to proceed with caution.
Speaking to ESPN this week, Cousins claimed he would be more than happy to return to New Orleans – but also left the door open on a potential departure.
“I don’t plan on rushing through this process,” he said.
“I’m going to make the absolute best decision for DeMarcus Cousins. We’ll see what that is.
“As of right now, I don’t really know. I can’t answer that.
Would I like to go back to New Orleans? I’m very open to that. I love what we created. I love what was created after I went down. I would love to be part of it.
“But I’m going to do what’s best for me, and I feel they’ll do the same.”
It comes after long-time Lakers target Paul George caused a shock by opting to sign a four-year $137m extension with the Oklahoma City Thunder.