Former chief Marina Granovskaia left her post following the departure of Roman Abramovich earlier this year, ending a nine-year association with the West London club.
Granovskaia was named the Best Club Director in European football at the 2021 Golden Boy awards, but Thomas Tuchel took on a leading role in transfers following her exit.
However, Boehly quickly decided that Tuchel was not the right fit for his long-term vision in London, and the German coach was relieved of his duties last week after 100 games in charge.
Having now hired Graham Potter on a five-year contract, Chelsea owner Boehly is now aiming to conduct another reshuffle upstairs with the appointment of a new advisor.
According to The Times, the Blues chief has made contact with Campos over a potential partnership in West London, only a couple of months after the 58-year-old joined PSG.
The report adds that Boehly and Potter discussed the appointment of a sporting director during managerial talks, and the former is "unhappy" with the current setup of the Chelsea squad.
The idea of Campos working with both PSG and Chelsea has supposedly been floated, with the Portuguese already juggling duties at the Parc des Princes with his Celta Vigo role.
However, with PSG and Chelsea potentially coming into competition for the same transfer targets, such an agreement is unlikely to come to fruition.
Campos spent time with Real Madrid, Galatasaray, Lille and Monaco before heading to PSG, where he reunited with Christophe Galtier after their successful stint at the Stade Pierre-Mauroy.
Galtier and Campos oversaw Lille's 2020-21 Ligue 1 title win, and the pair have conducted a major summer reshuffle of the Parisiens squad after tying Kylian Mbappe down to a new contract.
The French champions largely focused on adding to their midfield ranks with youthful talent, signing Fabian Ruiz, Carlos Soler, Renato Sanches and Vitinha.
Striker Hugo Ekitike and defender Nordi Mukiele also arrived at the Parc des Princes, while a plethora of fringe players such as Mauro Icardi, Julian Draxler, Idrissa Gueye and Layvin Kurzawa were moved on.
PSG continued their unbeaten start to the new season with a 1-0 win over Brest on Saturday thanks to Neymar's goal, while Chelsea's Premier League clash with Fulham was postponed in the wake of Queen Elizabeth II's death.
Chelsea are back in action against Red Bull Salzburg in Wednesday's Champions League Group E match, while Les Parisiens are up against Maccabi Haifa in Group H at the same time.