Byrnes has already met with the Demons, and a decision could be made by the end of the week.
General manager of list management Tim Harrington said that key club officials were “doing a mountain of work and information gathering” behind the scenes.
“We think we’re further advanced this year than in previous years with other clubs and player managements and player agents,” he told melbournefc.com.au.
“Increased resources at the club have meant that we’re able to cast our net wide.
“Coupled with the compensatory picks that we activated at the start of the year, this gives us the opportunity to improve the list substantially.”
The Demons have also been linked with attempting to secure Collingwood 2010 premiership players Chris Dawes and Sharrod Wellingham via the upcoming trade period.
Aside from the possibility of securing Byrnes, Melbourne doesn’t expect to land any other players this week.
“No other deals [are likely to be] done this week - none,” Harrington said.
Harrington said free agency had added “layers of complexity” to the trade period - from both a player personnel and financial sense.
“For example, someone like Brendon Goddard demands a pretty penny and clubs would be budgeting to keep their free agents, knowing that they’re a chance to lose them if they’re unrestricted,” he said.
“Then you’ve got three days to determine whether you match the offer for a restricted free agent.
“Then you’ve got to turn your attention to trading … and this can create scenarios that have to be thought through very carefully.”
Meanwhile, player development and strategy general manager Todd Viney said the club was open to “a lot of things” regarding its No. 3 and No. 4 picks in the November NAB AFL Draft.
“The most important thing is talent, and we’ve got to try and make sure as best we can to get that really right,” he said.
“We can’t afford to make mistakes with those picks, and there are a lot of things to take into consideration. But we’re certainly looking for some really good talent to come in and help us move forward from next year.”
Viney said he would always select talent over needs early on, but he acknowledged that particular attributes needed to still be considered early.
“There is midfield talent right at the front end,” Viney said.
In regards to how he feels about son Jack being a potential father/son prospect and the speculation about his playing future, Viney said it was “an interesting scenario”.
“We have a pretty experienced recruiting staff and list management staff that will be making big calls on that - it won’t be my decision in the end, it’ll be the list management and recruiting staff’s opinion,” he said.
“That’s just the way we’ll unfold.
“We knew right from the start that it was going to be like this, and it’s going to go down to the wire.”