Crowther, who is Trinity's youngest-ever Super League forward, after debuting as a 17-year-old in 2014, has been offered a two-year deal.
The 21-year-old became a first-team regular during last season's Super Eights, making five appearances.
He spent the majority of last campaign on loan at Dewsbury Rams but has played nine times for Trinity in 2019.
Winger Kershaw and prop Gwaze have both been offered a one-year deal.
Kerhsaw burst onto the scene last month, scoring a try on debut as Trinity defeated Leeds Rhinos 26-24 on Easter Monday.
Zimbabwe-born Gwaze joined Trinity's academy from Halifax's youth side and signed a first-team contract in May last year.
The trio follow Ryan Hampshire in being offered a new deal by Trinity. The half-back has been presented with a renewed three-year deal, which is currently being considered.
Meanwhile, it was confirmed yesterday that forward Justin Horo has left the club by mutual consent, after spending one and a half seasons at Belle Vue.