The 27-year-old is overseas and yet to commit to the Demons, who have declared they want him to stay.
"Col has been offered a deal from us - we're obviously very keen to keep Col, he's got all the information from us and he has a deal on the table," football operations manager Josh Mahoney told SEN on Wednesday.
"He's overseas at the moment and he's taking his time and we hope we get a decision in the not too distant future."
Sylvia has said before he would like to remain with the Demons but is yet to formally confirm that.
Mahoney said the club expected him to field offers from rival clubs but hoped he would re-sign with them, as Jack Watts did on Tuesday.
"We think [Sylvia] is going to be a key player for us in the midfield," he said.
"He's now played over 150 games and has been at the club for a long time.
"We think he can really help our young guys coming through.
"He's got a deal there, but he's obviously got a decision to make."
The Demons have also expressed interest in Sydney Swans assistant coach Stuart Dew joining as new coach Paul Roos' senior assistant and possible successor as early as 2016.
Mahoney said Dew had contacted the club about the role but the Swans had halted talks.
"With this process, we've said all along we're taking phone calls from people interested in the role and Stu, like a number of other coaches rang me expressing interest in the role," he said.
"We then go and speak as a group if we then want to talk to the person who has rung.
"We obviously want to speak to Stuart Dew. He's a candidate we'd like to speak to, and at the moment the Swans are blocking that and that's their right to do that.
"We have had other coaches go through the process who have been in contract; we've contacted their clubs and their clubs are obviously very happy to let them go through."
Watts signed a three-year contract extension with the Demons on Tuesday that locks him into the club until the end of 2016.
"Now he mentally knows what he needs to do to be an AFL footballer; it all seemed to be coming together for the second half of this season," Mahoney said.
"Hopefully under Paul Roos' coaching, Jack can just get better and better."
Twitter: @AFL_JenPhelan
