No charges had been announced by the AFL as of Monday night.
Bombers heavyweights including chairman Paul Little and chief executive Ray Gunston gathered at Windy Hill on Monday, sparking speculation an announcement might be imminent.
It has been more than a week since the AFL received ASADA's interim report into the club's suspect 2012 supplements program, which the anti-doping watchdog has been investigating.
But despite the pressure on him and key Essendon figures like head coach James Hird, Thompson said he would resist any pressure to resign - and most likely so would Hird.
"I don't want my reputation tarnished by this," Thompson told Fox Footy's AFL360 program on Monday night.
"You can't (resign) ... it's your whole life. It's not just your life. It's your kids, your family, it's going to be remembered forever.
"I don't want it on my tombstone."
The ASADA and AFL investigations into the Bombers started in February, and have dragged on throughout the season.
Should the league announce charges against the club and personnel on Tuesday, the Bombers are expected to have 14 days to respond.
After holding a top-four position for the most of the season, the on-field toll is starting to tell on the club.
Essendon has lost its past three matches by a combined total of 188 points, and slipped to seventh.
Possible penalties for the Bombers could involve a fine, loss of draft picks, and stripping of premiership points, which could jeopardise Essendon's hopes of playing in the finals.
