The Lakers are believed to be leading the chase for Davis ahead of the February 7 trade deadline.
The New Orleans Pelicans star shares the same agent as Lakers star LeBron James, raising the likelihood that he will move to LA.
It has been suggested that Davis may not join in this period and could instead wait until free agency in 2020.
Lakers are attempting to build a dynasty with LeBron, and acquiring Davis would go a long way to doing that.
But NBA pundit and former star Barkley has urged Silver to put a stop to the trade.
“Adam Silver needs to block that trade,” Barkley said.
“I don’t like what the Lakers are doing. I don’t think it’s right.
“Rich Paul got mad at me because I said a month ago, I said, ‘Oh the fix is in. Anthony Davis is going to the Lakers.’
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“This was before all these rumours started.
“He didn’t like me saying the fix was in. The fix has been in.”
Another former NBA star believes Davis is doing all his can to make the switch to the Lakers.
“I think for the Lakers they obviously want to get it done,” RexvChapman said.
“Watching Anthony Davis just then, I don’t know if I can remember a player in a long while that has been more ready to get up out of where he is.
“He’s ready to go. You can see it in every answer he gives.
“He’s a guy who sacrificed, he plays winning basketball and I think he’s ready to get back to that.”
Davis could be in action for the Pelicans tonight as they face Indiana Pacers.