The experienced defender is under contract with Atleti until the end of the season, but is thought to be tempted by the security of an extended deal at the French champions.
According to the aforementioned source, PSG have offered the Brazilian a two-year deal with an option for a third that would see him double his wages as they search desperately for cover for Layvin Kurzawa.
Although he is happy in Madrid, the size of the offer has given Luis no option but to seriously consider it, with a meeting with Simeone and Marin that is set for some time on Tuesday likely to be key to his final decision.
Simeone, for his part, retains faith in Luis and sees him as an important squad member and having personally convinced Diego Godin and Antoine Griezmann to reject overtures from elsewhere in the past there is no reason to think that he could not do the same again.
The left-back started his side's 1-1 draw with Valencia on Monday, with Lucas Hernandez having returned late following his World Cup exploits.
The lateness of the bid would leave Atletico with just 10 days to hunt down a substitute, a task which is complicated by the fact that Italian and English sides can no longer replace outgoing players and are thus unlikely to sanction exits.
Whilst Luis' name is on PSG's wishlist he is by no means the only one, with Bayern Munich's Bernat also thought to be an option.
One way or another, Filipe Luis is likely to have come to a decision by the time he finishes his discussion with Marin and Simeone on Tuesday. Atletico or PSG?