Jones was due to become a restricted free agent at the end of the 2015 season, but AFL.com.au understands the parties are in talks to extend the 26-year-old's stay at the club.
The star midfielder signed a three-year deal when tying up his last contract from 2012 to 2015 and it is understood Melbourne's offer is set to be lengthier this time around, seeing him remain a Demon for life.
Jones, who recently won his third consecutive best and fairest award, enjoyed his best year to date in 2014.
The Demons co-captain achieved career-highs in disposals (27.7 per game), tackles (5.2), clearances (6.2), contested possessions (11.6) and uncontested possessions (16.1).
In addition, Jones was second in the competition for total disposals (610) and fourth in clearances (138) and was desperately unlucky not to earn an All Australian nomination in the squad of 40.
Jones has played 179 games in nine seasons with the Demons after being drafted with pick No. 12 in the 2005 NAB AFL Draft.