The France international is one of Harry Redknapp's prime transfer targets, although he has doubted the likelihood of a deal.
The latest reports in France suggest a bid of £6million will be enough to tempt Lyon into a sale.
Pompey are rumoured to have offered close to that figure already and an increased bid is on the cards.
Lyon chairman Aulas has confirmed that the Premier League club are currently the favourites to sign the former Liverpool youngster.
"Portsmouth are in the driving seat," Aulas told the French media.
"Diarra could leave in the coming days."