Randle and the Wildcats recently advanced to the NCAA finals, falling to the Connecticut Huskies, 60-54.
Early entry candidates, such as Randle, have until April 27 to declare for the draft.
Randle denied recent reports that he would leave Kentucky for the NBA.
[I don't know] who reported what but I haven't made up my mind about the draft yet. Haven't even talked to my family about it. So it's all false.— Julius Randle (@J30_RANDLE) April 9, 2014
The 6-foot-9, 19-year-old Randle is projected to be a top-five pick. Through 40 games with Kentucky, he averaged 15 points and 10.4 rebounds a game.
The Lakers (25-53) have the sixth-worst record in the NBA with one week left in the regular season.
Should Randle declare, he could be in the Lakers' draft range.
Freshmen forward Andrew Wiggins and center Joel Embiid have already announced they'll leave Kansas. Duke prospect Jabari Parker has yet to reveal what he will do.
Once a player declares for the draft, they have until June 16 to withdraw and return to school if they haven't hired an agent.
The draft will be held on June 26 in New York.