The club have published photos via social media of their young striker out working in the sunshine wearing the club’s current green training kit.
He has been out of action for almost eight months after suffering a knee injury early in his first Premier League start, at home to Aston Villa.
The photos were clearly positive and showed him running alone. In one, he appeared to be turning.
But the Seagulls are still likely to face a decision in terms whether they are well enough equipped up front as they head into a busy campaign.
Tzimas will hope to play a big part but it appears it will be the second successive year in which he is playing catch-up in the early weeks.
Head coach Fabian Hurzeler said at the time of the injury: “I hope he will be back in pre-season.”
Tzimas first ventured back on to a training pitch in mid-April.
Sporting an impressive scar just below his right knee, he told The Argus at the time: “My recovery goes very well. In a week I will start on the pitch, to go out on the pitch and then slowly, slowly, step by step.”
Danny Welbeck looks set to lead the Albion attack into the new season, refreshed after a summer of rest and then his own personal training before the return to Lancing.
Charalampos Kostoulas, like Tzimas, was among the new arrivals who trained apart from the main group this time last year as they got used to the demands set by Hurzeler and his staff.
Kostoulas should be more up to speed by now and the expectation will be that he is better placed to make an early impact in the coming campaign.
Georginio Rutter can play as a false nine and will look to improve on what he offered last season.
And there is still the unknown factor of Evan Ferguson in terms of when he will be ready to play and what role he will have.
But, as with most transfer windows, fans will be looking out for a new addition at the sharp end of their team.