Marquis is on loan with the Gills and scored his eighth goal in 17 appearances for the League One club in a 1-0 victory over Bradford on Saturday.
Former Lions boss Ian Holloway was prepared to let the 22-year-old leave on a free transfer in the summer but Neil Harris, in charge for the remainder of the season, has been closely monitoring his performances.
Gillingham had hoped to sign Marquis on a permanent basis but Edinburgh thinks that may no longer be possible.
“It is difficult because he is not our player but there have been talks. I think Millwall have made him a new offer of a contract,” said Edinburgh.
“When players like John Marquis come to the club and have the impact that he has, then you are going to be interested in him, there is no doubt about that.
“We have spoken to John on numerous occasions. He is comfortable here, has fitted into the group well and he has eight goals now.
“If there is something we can do then we are trying hard to do it. When you have someone on loan, if they have a spell like he is, it becomes a different equation.”