Andy Hessenthaler stood down as Gills boss on Tuesday after failing to guide the club to the League Two play-offs.
Scally told the club's official website: "I get numerous applications and numerous agents who call me with many names they represent and I'm getting CV's at a rate of 10 a day at the moment.
"That's quite healthy and a testament to the football club that so many people want to manage here. I'm quite encouraged by that and there are some very interesting people putting some very interesting proposals to us at the moment.
"My view is that we will wait a week or so, I will try and meet one or two people I want to talk to this week, and already certain interviews have been set up around the country which I will be doing.
"We will then probably have a board meeting towards the end of May or in the middle of May and assess a shortlist of 10 or 12 people to determine who we want to see for second interviews."