Dover could miss out on defender Danny Collinge after he linked up with Dagenham.
Collinge, who was released by Colchester in the summer, has impressed after featuring for Whites in pre-season.
But the lure of remaining in full-time football with National League rivals Dagenham could mean Dover boss Andy Hessenthaler misses out.
"Dan wanted the opportunity to trial at Dagenham," said Hessenthaler.
"They are full-time and he comes from Essex so if they offer him something I can understand if he accepted it."
Dover still have space for a couple of players in their squad with Hessenthaler looking defensively and for an attacking player.
But the Whites boss is adamant he won't sign anyone who he doesn't believe is the right fit.
Will Moses has been missing with a knee injury while Reda Johnson (calf), James Caton (groin) and Aaron Cosgrave (hamstring) all missed Monday night's friendly at K Sports.
"We've got to get it right," he insisted. "That's why we let the trialists go after last weekend, as something told me that they weren't for us.
"We've got 17 players at the moment, we know what the budget is - we can only have 18 or 19 players in the squad and if we need a couple of loans we can get some help, like we did with the keeper Adam Parkes from Watford.
"Because we've got such a small squad, they've got to be right.
"We looked at a couple at the weekend who were very close but we're looking for something different to what they gave us.
"It's difficult when you are a trialist at times, you can't give them enough minutes because you need to take care of your squad as well but then you need to make a decision."
Dover continued their winning form with victory over Folkestone on Saturday.
The result didn't matter to Hessenthaler but he accepted it was a disjointed display as he continues to finalise his squad.
"It was frustrating as it got disjointed but it will be like that until we get something settled," said Hessenthaler.
"I thought we could have been more high tempo at times, we didn't do that or have enough movement.
"But, having said that, we haven't done any work on the shape yet and we played two different formations
"When we play the likes of Stevenage, Tonbridge and Watford we'll get more clues to where we are at."
Dover host Stevenage in a friendly this Saturday at Crabble.