Jamie's family, including his daughters Corinne and Anelise, as well as Anelise's mother, Kristin Grannis, were all in Chicago both Saturday and Sunday to spend time with Foxx during his continued care.

While we still don't know exactly what happened to Jamie or why he's there ... we know the facility specializes in stroke recovery, traumatic brain injury rehab, spinal cord injury rehab and cancer rehabilitation.

One source tells us Foxx arrived at this facility in Chicago in late April -- after initially getting treatment in an Atlanta hospital -- and sources connected to Jamie tell us he's "recovering well."

Jamie's loved ones appeared to be in good spirits over the weekend, and there are signs he's alert and active -- including the fact Kristin left the center with Mother's Day flowers and a balloon.

Also, Anelise had her guitar with her, so you gotta imagine she was able to play and sing with her dad ... a good sign considering how important music is to Jamie.

Corinne, who has been by her dad's side from the start of his medical troubles, was also joined by her boyfriend on at least one of the visits, cracking a smile ... which, hopefully, is a marker of positive things happening for Jamie.

At the end of last week, Corinne announced her father had been out of the hospital for "weeks" and was "recuperating" -- she also mentioned he was playing pickleball.

While it's clear he's still getting treatment, the rehab center is obviously encouraging for Jamie's overall progress -- and the facility offers an adaptive sports and fitness program -- which could explain the game of pickleball.

As we reported, Jamie was first hospitalized April 12 in Atlanta for what his family called a "medical complication" ... but all seems to be headed in the right direction.