Hampton & Richmond hope to welcome Pompey as part of their summer pre-season schedule.
Jamal Lowe and Nicke Kabamba this month departed the National League South club for Fratton Park for undisclosed fees.
According to Beavers boss Alan Dowson, his Blues counterpart has also verbally agreed to a friendly.
Although nothing has been put in writing, Dowson is banking on Paul Cook keeping his pledge, thereby providing the non-league club with a further windfall.
And for Blues followers it would represent a trip to the 3,500-capacity Beveree Stadium set in Hampton, Middlesex.
Dowson said: ‘During the signing of Nicke, we did mention a pre-season friendly.
‘I think Paul Cook is a man of his word and he will do that.
‘We talked about them sending a side down and, although it’s not in writing, I think he will do that. It would be great for our club.
‘The dealings with Pompey during the sale of our two lads have been really good. Paul Cook has done everything straight, he hasn’t gone behind my back or tried to tap anyone up.
‘As soon as I met him I knew he is a manager who can get the best out of Jamal and Nicke.
‘I have been in football since I was 15, playing professional football at Millwall and Bradford, before entering the management game.
‘And it’s the first time I have walked away from talking to another manager thinking “I wouldn’t mind playing for this bloke”.
‘He has similar old-fashioned morals to me and I really like that about him.’
Hampton & Richmond are presently eighth in National League South, three points outside the play-off places.