The News understands the Championship club are casting an eye over the ex-Blues stopper as he bids to get back into the professional game after departing PO4.
Seymour, 20, was released by Pompey – along with a host of other youngsters – earlier this summer having made just a single senior appearance for the club.
He came on as a substitute in the Blues’ 5-1 EFL Trophy defeat at Peterborough in January.
Boro boss Shaun Gale had been casting an eye over the stopper as he searches for a new goalkeeper.
But now Seymour is presently on trial with the Rams in an attempt to earn a deal with Wayne Rooney’s Championship side.
Blues boss Danny Cowley has already boosted his goalkeeping pool, which was depleted by the release of Taylor and Craig MacGillivray – by signing Manchester City and Republic of Ireland ace Gavin Bazunu on a season-long loan.