The Blues have the centre-back high on their summer shopping list as a potential replacement for Matt Clarke.
Lockyer turned down a new deal at Bristol Rovers, admitting it was time for a new challenge elsewhere.
A number of Championship clubs are chasing the 24-year-old, but Pompey are hoping his former Memorial Stadium team-mate Lee Brown can persuade him to move to Fratton Park.
Lockyer ideally wanted his future decided before a potential call-up to Wales’ squad for the upcoming Euros 2020 qualifiers against Croatia (June 8) and Hungary (June 11).
After a six-day training camp in Portugal, Lockyer’s spot in Ryan Giggs’ 28-man set-up for the two games has been confirmed.
That means all of Lockyer’s full attention will likely be with Wales until after those matches have taken place.