Burnley boss Eddie Howe is being linked with the Portsmouth job.
The Sunday Mirror says Howe is believed to be keen to return to the south coast, where he spent most of his playing career with Bournemouth, a club he also managed.
That has alerted Pompey, with a source saying: "He is an ambitious young manager with a good track record."
Also in the frame is Molde coach Ole Gunnar Solskjaer, the Manchester United legend.