Crawley boss Steve Evans told the club website: "Danny Wilson put a proposal to me but that was rejected after I consulted with my bosses.
"Danny and myself have spoken a number of times since. It's now at the point that I must now be on speed dial on Danny Wilson's mobile phone."
Evans added: "On a serious note, Danny has confirmed he will be back to me after he has had time to discuss this further with his chairman. Whether this leads to an increased offer is not for me to guess."
Ademeno scored a hat-trick in the space of just four minutes and 12 seconds as Crawley won at Grays on 28 December.
He's very powerful and strong, is good with both feet and scores goals
Swindon boss Danny Wilson
Evans is not surprised there is interest in Ademeno, but insists he will only leave for the right price.
"There is no doubt that Swindon Town fancy the boy, but then again it is no surprise given his talent," he said.
"We are certainly not being greedy with our valuation of the boy and any offer that we receive will get our full consideration.
"Any deal obviously has to be right for Crawley Town Football Club and the bidding club but more importantly for young Charlie himself. Until such times as an agreement is reached we will all go about our work as normal.
"I have known Danny Wilson for a long time now and he has conducted his business on behalf of Swindon Town Football Club in a very professional way. This is nothing I would not expect from the man I know well."
Of his interest, Wilson told BBC Wiltshire: "You've just got to take a gamble sometimes.
"You don't know until you put them in whether they can step up. He's very powerful and strong, is good with both feet and scores goals."
Source: BBC Sport