The 19-year-old midfielder joined the Whites last summer from Manchester City on a four-year deal as Kalvin Phillips went the other way.
Gyabi was selected for England at the Under-20 World Cup, which took place earlier this summer, and he also scored a goal against Uruguay in the group stages.
He was handed his Leeds’ first team debut in November in an EFL Cup match and his first Premier League debut a month later against his former club Manchester City.
New head of football operations Underwood, the youth academy boss of the Whites last term, feels that Gyabi is a player about whom the club can be excited.
He stressed the 19-year-old English midfielder has been impressive on and off the pitch since he came to Elland Road.
“We’ve got a great depth of talent and I believe wholeheartedly that we’ll benefit from that in future”, Underwood was quoted as saying by the Yorkshire Evening Post.
“Having been with us now for a year, he’s [done] nothing but impressed in every sense on the pitch and off the pitch.
“[He’s a] great character and somebody that I think like many of those Under-21s that we have, we can be excited about.”
Gyabi has featured in Daniel Farke’s both pre-season matches so far and is expected to be handed sufficient game time in the upcoming Championship campaign.
