Rose has also been in "serious discussions" with the Cleveland Cavaliers about joining the defending Eastern Conference champions, but ESPN.com's Brian Windhorst and Adrian Wojnarowski reported the Lakers "are trying to entice Rose to sign with them, suggesting they can offer more playing time and money in a better environment."
USA Today's Sam Amick added Rose is "likely" to make a decision on his future this weekend, and that the Chicago Bulls could creep into the picture along with the Cavaliers and Lakers.
Cleveland and Los Angeles have their respective advantages, so Rose's decision will have to come down to whether he wants a more significant role at a higher rate or a shot at a ring.
With the Lakers, Rose would presumably form a point guard partnership with No. 2 overall pick Lonzo Ball and give head coach Luke Walton some peace of mind since L.A. is currently without a seasoned backup for the rookie.
If Rose opted for the Cavaliers, he would likely be doing so at a discount, as Wojnarowski and Windhorst noted Cleveland is likely to offer a $2.1 million veteran minimum contract.
Conversely, heading to Northeast Ohio would give Rose a chance to vie for a title and offer some bench reinforcements for a second unit that ranked 28th in scoring (29.1 points per game) last season.