The French champions have been linked with Gueye all month and had a £21.5millon bid rejected earlier this week.
That led to speculation Gueye had handed in a transfer request in order to force through a move, urging the Toffees to reach a compromise.
His absence from the Huddersfield Town game due to a “minor injury” only fuelled speculation he could be on the move.
Reports earlier this week suggested Everton were ready to reach an agreement, with Marco Silva even threatening to resign over the issue.
Now it seems Everton are digging their heels in and refusing to entertain the notion of letting Gueye leave.
The board are reportedly unhappy with PSG’s behaviour and their refusal to meet their asking price, while simultaneously seeking to put pressure on the club and the player before the deadline.
As a result they are now refusing to entertain any more offers and even considering reporting the Ligue 1 champions for their behaviour.
And given there is little time to bring in a replacement, they are also unlikely to sanction any deal that would leave the squad short in midfield.
Meanwhile PSG have already added one Argentinian midfielder in Leandro Paredes and are very close to adding Luciano Acosta as well.