The former England defender has been a regular at the Blues’ Hilsea training ground in recent weeks.
A friend of manager Kenny Jackett, he has been helping to coach Pompey’s defensive players and was in attendance yesterday as the team prepares for tonight’s Checkatrade Trophy game at Charlton.
Moyes was named as Hammers manager this morning following the sacking of Slaven Bilic.
The Scot is expected to name his backroom staff in the coming days, with Pearce linked with a move back to a club where he made 45 appearances.
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In an interview with Talksport yesterday, Pearce said he would be keen to talk to the club if the chance arose.
‘I’ve had no contact with West Ham,’ he said.
‘But if I had contact with them I would certainly go and talk to them.
‘I really enjoy doing the media work, but then again I enjoy coaching – I’ve been at a club today coaching.’