Noor Alfallah, who is 52 years his junior, first hooked up with the singer at a private flat in the Parisian suburbs two Sundays ago.
The next day a chauffeur drove her back to her hotel. They repeated the routine on Tuesday and Wednesday.
US-born socialite Noor, 22, watched the Stones perform at the city’s U Arena the next night and they enjoyed three more dates last week.
A source said: “Mick still has his legendary charm but even the band were surprised someone as young and beautiful as Noor came to Paris to see him.
“They are both single and seemed to have a lot of fun together, so everyone just let them get on with it.
Noor Alfallah, 22, watched The Rolling Stones perform in Paris and has been on dates with Mick Jagger
Noor Alfallah, who has hooked up with Mick Jagger, is pictured by a car in Paris as she heads back to flat
“Mick is showing absolutely no sign of slowing down. He certainly had a smile on his face and famous twinkle in his eye.
"Noor is very confident and well educated so she fitted in well at all the upmarket places they went together.”
Great-grandad Mick was seen arriving at her hotel the day after she watched him perform.
A week ago they had dinner with his backing crew at the Caviar Kaspia.
The following night they dined alone at La Stresa.
Noor, whose dad is Kuwaiti, was pictured in leather jacket, skirt and thigh-length boots as she left behind Mick, who was flanked by guards.
The Stones finished their 14-date No Filter tour in Paris on Wednesday.
Jagger is believed to have met film graduate Noor through a mutual pal, producer Brett Ratner.
Mick is dad to eight children with five women.
His youngest is ten-month son Deveraux by ballerina ex Melanie Hamrick, 31.
Last night Noor declined to comment.