The Sky Blues were granted permission to hold talks with Pressley on Wednesday having identified the Scot as their number one choice to replace Mark Robins following his switch to Huddersfield three weeks ago.
And they have spent the past 24 hours attempting to iron out personal terms as well as a compensation package with his current Scottish First Division employers.
Coventry development director Steve Waggott said: "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."
City are looking for their third permanent manager of the season and fifth in total following Robins, Andy Thorn - sacked in late August - and caretaker bosses Richard Shaw and Lee Carsley, who has won three and lost two of his five matches at the helm in recent weeks.
Former Scotland defender Pressley, 39, enjoyed a brief playing spell with the Sky Blues during the 1994/95 Premier League season.
