Sources have told the Bolton Evening News that Dacourt, who will be 31 next month, is due for fresh talks with Wanderers this week.
The former France international, who is surplus to requirements at Roma, priced himself out of a move to the Reebok earlier in the summer, when he was being touted as a target for Arsenal.
But Dacourt, who had spells at Everton and Leeds and has changed hands for fees totalling more than £21 million during his career, is believed to be lowering his demands as he becomes more desperate to find a new club before the August 31 deadline.