The Blues are ready to bring in the left-back, who is a free agent after leaving Priestfield this summer.
Football Insider report the 25-year-old is set to have a medical next week ahead of completing a deal.
The former Spurs man has been linked with Pompey in the past and was with Gillingham for two years, where he scored nine goals in 92 appearance after joining the club permanently.
GIlls boss Steve Evans said there was still a contract offer on the table for Ogilvie if he wanted to remain with his old side, where he has been training this summer.
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