Administrator Andrew Andronikou revealed the Blues have already received half a dozen applications for the Fratton Park hot seat vacated by Avram Grant.
Steve Cotterill has also been put forward. In addition he has been installed by bookies as one of the early favourites.
Of those currently at Pompey, Groves has told the club he wants to remain as a coach, while Andronikou believes keeper David James is not yet ready.
Regardless, the administrator insists there is no rush to name a manager, with finalising the CVA by the middle of June the priority.