The League One club are looking for their third permanent manager of the season following the exit of Mark Robins to Huddersfield Town.
The Sky Blues, who were granted permission to speak to Pressley on Wednesday, are understood to be ironing out a compensation package with Falkirk for the former Scotland defender.
Coventry development director Steve Waggott told Sky Sports News: "We've held very positive talks with Steven Pressley and Falkirk today (Thursday) and they are progressing well.
"We will continue working on the deal in order to reach a conclusion that is good for all parties."
Pressley played for Coventry between 1994 and 1995.