The club had been given a May 30th ultimatum to show evidence of a much-discussed takeover by an American consortium, or that they had the finance in place under current owner Mick Crossan to continue through the 2023-24 season.
The RFU's club financial viability working group have a meeting scheduled on Tuesday evening ahead of making a recommendation to the RFU board on Wednesday.
Local media reported that the recommendation will be for a week's extension, subject to proof that the players' latest salaries have been paid following delays last month.
Irish, whose fifth-placed finish was their best since 2008-09, are hoping to avoid following in the footsteps of Wasps and Worcester, who both went into administration late in 2022 and were expelled from the league.
