Aston Villa's future looked bright last season when they had both Marco Asensio and Marcus Rashford on loan.
Unai Emery's side made it to the quarter-finals of the Champions League before losing to eventual winners Paris Saint-Germain.
Villa were also hunting qualification for European football's top competition again.
However, they ended up losing to Manchester United on the final day and just missed out on finishing in the top five of the Premier League.
Rashford then joined Barcelona, but Asensio could still join Villa permanently.
L'Equipe has reported (translated from French) that PSG "is close to reaching an agreement with Aston Villa for the transfer of 29-year-old striker Marco Asensio."
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Marco Asensio could save Aston Villa's season
Villa have had a disastrous start to the new season, they drew 0-0 with Newcastle United before losing 1-0 to Brentford.
The Midlands side has had a difficult transfer window due to financial constraints of missing out on Champions League qualification.
Their only notable signing has been Evan Guessand from Nice, but he has so far played just 15 minutes of football for Villa.
Asensio scored eight goals, with one assist, in 21 games for Villa last season. Emery will be hoping the Spain international can have a similar impact again.
Aston Villa news and related links
- Morgan Rogers dismisses exit talk amidst Premier League transfer speculation
- Aston Villa forward agrees surprise season-long Serie A loan deal
- Aston Villa handed transfer blow in pursuit of Chelsea star