Heat president Pat Riley and coach Eric Spoelstra will be there to make the pitch, the source said.
Miami, though, certainly will have competition for the free agent center.
The Bulls met with Gasol on Thursday in Los Angeles, with Joakim Noah part of Chicago's contingent, sources told ESPN.com's Marc Stein.
ESPN reported Wednesday night that the Oklahoma City Thunder duo of Kevin Durant and Russell Westbrook made a strong case to Gasol during a face-to-face pitch Wednesday in Los Angeles. Thunder general manager Sam Presti also spoke Wednesday by phone to Gasol, ESPNLosAngeles.com reported. The Thunder have emerged as a surprising front-runner despite their financial limitations, according to sources close to the process.
One source described Gasol as "opening up to the possibility" of joining forces with Durant and Westbrook even though Oklahoma City is limited to roughly $5 million in spending cash under the luxury-tax line at present.
However, the Lakers can pay Gasol more than any other team, and his fondness for the city and playing with Kobe Bryant should not be discounted. If the team can add to its roster with Carmelo Anthony, sources said, Gasol would be far more inclined to re-sign with the Lakers.
Gasol met with the Lakers on Tuesday, and according to one source, the meeting "went very well."