Bartlett has praised Craig's commitment since taking over the coaching position but would not be drawn on the selection process or when an appointment would be made.
The discussions with Craig are understood to have been relatively informal, with the caretaker coach saying publicly he would not put his hat in the ring until he knew what the club was after.
Craig is yet to give a public indication he is convinced he has the desire to coach again.
The club interviewed Rodney Eade and Mark Williams in recent weeks and also remains open to the possibility of Paul Roos becoming a candidate.
Bartlett told AFL.com.au that the decision on who would next coach the club was something Melbourne had to get right.
He said the club needed "a coach that has a real track record of developing players and programs".
Bartlett said that focusing on selecting an experienced coach seemed to make sense and once the decision was made, other appointments would fall into place.
Speculation continues about whether Melbourne deserves a priority pick after just 34 wins in its past 152 games, but the new president said he was more focused on choosing the right people in the right positions.
Appointed to the position on Friday after joining the board in July, Bartlett said he wanted to stabilise the administration so the focus could return to the players.
He hopes to be a low profile president but has been frank in his assessment of the club's culture.
Bartlett said was not apparent to him what the club stood for and its core values were not obvious.
He said the club needed to develop a harder edge in the way it did things on and off the field.
His comments to members on Sunday that he thought the club's culture had been soft had been well received.
"I have had a number of long standing members saying it's great that you said that because everyone talks about it but no-one has actually said it," Bartlett said.
"The vision is to become an elite driven sporting club that is very professional in everything we do on the field and off the field."
The president addressed the players on Tuesday and told them football and their development would be the club's number one priority.
Speaking not long after Aaron Davey's retirement he also reminded players their football careers went quickly so they had to make the most of the time.
Bartlett began barracking for Melbourne four years ago after arriving in the city from Perth.
The former West Coast Eagle (four games in 1987) and East Perth player was introduced to the Demons "through the mate of a mate" and then joined the Foundation Heroes and travelled on Darwin fishing trips alongside key supporters.
He said he loved the colours, the song and the history of the club.
Bartlett had resisted suggestions 18 months ago he should consider joining the board but once he finished his three-year tenure as a managing partner at Clayton Utz, time allowed him to take a position on the board.
He is taking a keen interest in the board redevelopment that is being managed by a nominations committee.
He said the committee would be in touch with all the people who had nominated but was focusing on those with skills in finance, culture and people and brand development.
Quietly spoken but with a serious football background, he laughed at the suggestion he was courageous to take on the job.
"I felt with my business background and the challenge that Melbourne has got … when I was actually put forward I thought about it: great challenge, great brand, great bunch of people.
"I thought I could make a difference basically and that is what I hope to do," Bartlett said.
