Tony Adams has been given three games to save his Portsmouth job.
The Sun says a run of eight Premier League games without a win has seen them plunge to within one point of the drop zone.
The FA Cup holders were also booted out of that competition by Championship outfit Swansea.
It prompted talks at the weekend between the club's owner Sacha Gaydamak, from his home in Israel, and executive chairman Peter Storrie with Gaydamak's pal Avram Grant - a former director of football at Fratton Park - being lined up as a potential replacement.
Gaydamak is keen to sell the club and is concerned that the threat of relegation could scupper any prospective deal.
But Adams, who only last month was offered a way out as manager of Feyenoord, has now been given three games to get back to winning ways.