The American investment group Arctos Sports Partners is the frontrunner to buy a minority stake in Paris Saint-Germain and a deal could be concluded within months, the Guardian understands.

Arctos holds a stake in Fenway Sports Group, which owns Liverpool, and acquired a £29.2m portion of the Serie A club Atalanta last year. If the purchase of shares in PSG is completed it is expected to take a stake of between 5% and 15%, with the club valued at €4.25bn (£3.7bn).

Although an Asian group has also held talks this summer over investing in PSG, Arctos’s longer-standing interest is among the factors that puts it firmly in the driving seat. It will be the first time Qatar Sports Investments (QSI), the club’s owner, has opened up equity to another party and the move is aimed largely at bolstering PSG’s ability to compete with Premier League clubs on the European stage.

There is no intention for fresh investment to signal an off-ramp for QSI, which became the club’s sole owner in 2012. PSG have won all bar two editions of Ligue 1 since then but, despite vast outlay on an all-star cast of performers, are yet to win the Champions League title they crave.

An injection of funds and expertise from Arctos – which also has significant interests in clubs in Major League Soccer, Major League Baseball, National Hockey League and National Basketball Association – is designed to help them to keep pace. Although PSG’s resources vastly outstrip their competition at home and many continental rivals, domestic television income falls far short of even the Premier League’s bottom-placed club.

Any investment from Arctos would provide QSI, which bought PSG for about €100m, with a huge return. It may also boost them in solving the longstanding problem of where to make a long-term home.

PSG do not own the ageing Parc des Princes, with a capacity of 48,500 not in line with their ambitions. They have not succeeded in attempts to buy the venue from Paris’s city council and are unwilling to invest in its expansion and modernisation unless a deal can be reached. The standoff has been viewed as a barrier to external investment and other options, such as a new ground or purchasing the Stade de France, are being actively explored.

PSG are keen to move on from the saga surrounding Kylian Mbappé, who has been barred from training amid fears he could leave for Real Madrid on a free transfer next summer. It will prove difficult, however, to shift the narrative if the situation is not clarified swiftly: Mbappé is a talismanic figure in French football and his departure would mean two thirds of the feted Mbappé-Neymar-Lionel Messi front three will have left. There is also speculation over Neymar’s future before their opening match of the campaign against Lorient on Saturday.