On July 27, 2021, Kaye was traded, alongside a first-round pick in the 2022 MLS SuperDraft to the Colorado Rapids in exchange for $1 million in General Allocation Money and a 2022 international roster slot. He made his debut for the Rapids on August 7 against Sporting Kansas City. On August 21 Kaye scored his first goal for the Rapids, netting the game-winner in a 2–1 comeback win over Rocky Mountain Cup rivals Real Salt Lake. At the end of the season Colorado announced they had exercised Kaye's contract option, keeping him at the club through the 2022 season. Before the start of the 2022 season Colorado would announce Kaye would sign a 4 year contract extension, through the end of the 2025 season, with an option for 2026.
