"Dundee Football Club can confirm that Calum Melville has offered his resignation as director of Dundee Football Club," said a club statement.
"This will be discussed at a board meeting and, until then, no further comment will be made."
Dundee last month announced that Bob Brannan was standing down as chairman but stressed that he would be continuing on the board.
And Aberdeen-based businessman Melville publicly re-stated his financial commitment to the club.
He said that, although it would not be on the same scale as the £1.2m he is said to have already invested in the club, he would continue to bankroll them for the next three to five years.
But, earlier this month, Melville, who was head of the offshore division of Cosalt, was suspended from his post while management carried out a review of working practices.
He also resigned as a director of the marine safety company, although it stressed in a statement that it did not believe there had been any illegal activity.
It appears that Melville does not believe he now has enough time to devote to the football club and their board will now want to investigate what that means for his promised future cash injection.
His money helped Dundee significantly strengthen their squad last season, but the team allowed their lead in Division One to slip under Jocky Scott and successor Gordon Chisholm.
Inverness Caledonian Thistle eventually won the title and promotion to the Scottish Premier League.
Chisholm's side have also made a disappointing start to this season in Division One and, after a 0-0 draw with Raith Rovers on Saturday, sit in seventh spot, seven points behind leaders Dunfermline Athletic.
The news of Melville's intended resignation came on the day when Scott and former assistant Ray Farningham were due to take the club to an industrial tribunal.
However, that case - the pair were claiming more than £250,000 from Dundee following their sacking - was postponed until January.
Source: BBC Sport
Source: BBC Sport