West Ham value the player at £40 million, and it is understood that any club would need to come within £5 million of that figure to have a realistic chance of securing his signature.
Such an investment would represent a significant statement from the Brazilian club, but work has been ongoing behind the scenes in an attempt to force a breakthrough.
On Thursday night, sources indicated that a new approach from Flamengo was imminent.
Early information from the West Ham side suggested there was scepticism about whether their valuation would be met.
The exact figures on the table are expected to become clearer on Friday as discussions open up. With the Brazilian transfer window open until March, this is a situation that could yet drag on.
West Ham are currently involved in a relegation battle and would ideally prefer not to lose Paqueta at this stage of the season. There is also concern over how they would replace him.
Paqueta is currently dealing with a back issue, meaning he is not fully fit, but Flamengo’s interest has nonetheless turned his head.
Sources indicate that personal terms have already been agreed for a return to Brazil, leaving club-to-club negotiations as the main obstacle to completing a deal.
