And the new Westleigh Park boss insists the Blues could have first refusal on any upcoming talents they feel are better than non-league standard.
Doswell took charge of the Hawks last month after they parted company with Lee Bradbury following relegation from the National League.
Pompey have traditionally had a close relationship with their near neighbours, loaning some of their youngster to gain first-team experience.
The likes of Calvin Davis, Theo Widdrington and, more notably, Jack Whatmough have had spells at Westleigh Park in recent years.
Kenny Jackett’s men play their annual pre-season friendly against the Hawks on Saturday, July 13.
Doswell is hoping he can utilise the rapport between the two clubs by bringing in some of the fledgling talents at Fratton Park.
But he declared they must be good enough to make the National League South grade.
‘We’ll look to progress that (relationship) even more so,’ said Doswell.
‘It’s a huge thing for this football club to stay very close to Portsmouth.
‘When I played down at Havant many years ago, they’ve always had the relationship with the football club.
‘That’s been good with all clubs.
‘Also, in the same way, occasionally we’ll come up with a young one that they could have the first shout on. It can work both ways.
‘I know they always have a friendly here, which is in July.
‘That is the opening part of the relationship. But you’ve also got to be good enough.
‘Some of the lads at 18, 19 or 20, even at professional clubs, are not necessarily good enough to get into our starting XI.
‘You’ve got to be good enough.’
Doswell revealed he spoke with Kenny Jackett last summer when he was in charge at Sutton United about the possibility of organising a pre-season game.
And he feels the Pompey boss will have done a ‘phenomenal job’ if he leads them to League One play-off glory.
‘Kenny Jackett and I spoke last year, we were trying to get Portsmouth to come down to Sutton,’ added Doswell.
‘They came down the year before and we had a great friendly with them. He’s a really good guy.
‘If he can get Portsmouth into the Championship, he’s done a phenomenal job.’