Goalkeeper Dunn and winger Davis have indicated that they have other offers on the table while Johnson wants Beckwith to move closer to the town if he is to stay.
Johnson said: "I'm still discussing things with Chris, Liam and Dean but they need to make their minds up quickly.
"I've said to all three of them, how much do you want to be here and if they can convince me that they really want to be here then I will look at offering them something.
"With Liam and Chris their representatives have said that they have other options but I'm saying to them to make sure that there are other options because if there aren't then they might miss out on this one.
"Dean lives away from the area and I don't really want him driving up from Gillingham every day because I think it affects him so we are talking about the possibility of him moving up here. I want them to give me an answer quickly and I have given all three of them until Friday to make their decision and then we can think about any offers."
Source: PA
Source: PA