According to the club website, he met with Whites chairman Jim Parmenter on Wednesday to discuss Gillingham's request to open talks.
Dover are expected to release a statement on Thursday.
If it's going to be Hess, at least it's a clean start for everyone at the club
lancastergill
The Whites have insisted that a compensation package must be agreed before talks can take place, but so far nothing has been offered.
Hessenthaler, who managed the Gills between 2000 and 2004, has refused to rule out a return but previously insisted he would not submit an application for the job.
Mark Stimson resigned from Gillingham 10 days ago following their relegation to League Two.
Source: BBC Sport
Source: BBC Sport