The Hawks have made a £10,000 bid for Gosport Borough striker Justin Bennett.
It comes just a week after Borough offered £7,500 in an attempt to lure Hawks striker Matt Paterson back to Privett Park.
Bennett and Paterson formed a potent strike partnership for Gosport last season.
And it appears both clubs are keen to re-unite them as a pairing.
Bradbury insisted the latest bid was a genuine offer and had not made in retaliation to Borough’s move last week.
‘Gosport’s attempt to get Paterson back got me thinking,’ said the Hawks boss.
‘They formed a lethal goalscoring partnership last season, so it would be good to get them back together again.
‘Justin Bennett was the league’s leading goalscorer with 34 goals last season.
‘He is on fire again at the moment.
‘He has scored 11 goals already and he is right on our doorstep.
‘It is a no-brainer and it would be great if we could get him.
‘The offer is a good one for someone who is 34 years old.
‘We have earned some extra cash from our FA Cup run and the chairman has allowed me to make the bid.
‘Paterson enjoyed playing alongside him and they scored a lot of goals together.
‘We are not prepared to let Paterson go anywhere but it would be good to get them back together.
‘Admittedly, we have a lot of strikers at the club already.
‘But we can’t pass up the chance of getting someone of Bennett’s calibre.
‘It is a genuine bid and it would be fantastic if he was allowed to come to us.’
Borough chairman Mark Hook is yet to see the offer but insists Bennett won’t be leaving.
He said: ‘It won’t happen. I think it is just the Hawks playing mind games and shows how desperate they are.
‘We will remain professional and dignified, give it due consideration and then decline.’