The pair have featured in the wins over local non-league sides Bottesford Town and Winterton Rangers as they bid to win Iron contracts.
Another trialist, striker Mustafa Tiryaki, has left the club after failing to earn a contract.
Full-back Brogan left Rotherham United in the summer, a club where he has previously worked with Knill, while midfielder Green has been released by Peterborough.
United are unlikely to have any other trialists or signings in the squad for the trip to The Shay, although Knill is still trying to bring in players.
Cliff Byrne, Michael O'Connor and Garry Thompson have yet to feature in pre-season.
Defender Byrne will play no part in any friendlies as he works his way back to fitness from back surgery – he is likely to return to reserve team football once the season starts, with a September return penned in.
Knill said at the start of pre-season that winger Thompson was able to play a full part in training, but has yet to test the groin injury that kept him out for much of last season in a match scenario.
O'Connor has been linked with a move away from Glanford Park – the Iron have turned down a bid from Peterborough – and his continued absence has fuelled speculation over a departure.