According to reports, there is a good chance there could be an appointment before Saturday’s home game with Solihull Moors.
Failing that, Devon Live suggests the Gulls expect the club to have Kevin Nicholson’s replacement confirmed by Monday’s Vanarama National League trip to Woking.
General manager Geoff Harrop says it is vital the club make the right appointment after a poor start to the season.
“We have had an excellent response with applications, which shows that we’ve got a club here that people think highly of,” he said.
“I don’t want to put a definite time-span on an appointment, because we’ve got to take this decision carefully, and do our best to get it right.”
Stand in manager Robbie Herrera has suggested he would like to be considered for the role.
His first game was on Saturday, a 3-2 away defeat to Guiseley.
He said: "Right now I am doing the job, I have to say like anyone else if the powers that be decided that they wanted me to have it, I would be interested in it that is for sure.
"We will wait and see when that decision is made but I am happy to carry on until that happens."