The former Albion wideman appears back at full fitness following almost three years battling a serious knee injury and associated issues.
He has posted photos of himself working hard in Qatar.
March, who will turn 32 on Monday, said: “Working in the heat and ready for what’s next.”
Having made 300 appearances for the Seagulls, he is now keen to relaunch his career elsewhere.
Clubs across the country are back in pre-season and building their squads.
Adam Webster has also been seen putting in the summer work and has been speculatively linked with clubs including West Ham and Ipswich.
Joel Veltman has trained at his old club Ajax while waiting to secure a new club having turned down a new deal at Albion.
The right-back has been working with Jong Ajax, the club’s development team who play in the second tier.
Meanwhile, former Albion midfielder Yves Bissouma is using Fulham’s training complex to keep himself up to speed after being let go by Spurs.
Bissouma has made use of facilities at Motspur Park but there are conflicting reports as to whether that could lead to a deal at Craven Cottage.
Some Albion fans seemed keen for their club to re-sign the Mali midfielder when he ran out of contract at Tottenham this summer and was told by head coach Roberto De Zerbi he had no part in his plans.