The 22-year-old Ghanaian midfielder has spent the majority of his City career away on loan at Norwegian side Stromsgodset.
A former Ghana Under-17 international, Adjei-Boateng joined City from the Right to Dream Academy in his homeland back in 2011 but has yet to make an appearance for the club after failing to secure a UK work permit.
The 22-year-old has been playing plenty of first-team football in the meantime, however, having spent the past four-and-a-half seasons on loan at Norwegian top-flight side Stromsgodset.
As well as scoring 18 goals in 101 total appearances, the highly-rated youngster helped the team win the Tippeligaen title ahead of domestic giants Rosenborg in 2013 and regularly featured in the Europa League qualifying rounds during his time away in Scandinavia.
He recently returned to City following the conclusion of the Norwegian campaign, which saw Stromsgodset finish seventh in the league, but is now reportedly set to head to the USA to join the Rapids on a permanent deal which could be completed by early next week.
Pablo Mastroeni’s side have been on the hunt for a replacement for the impactful Jermaine Jones over recent weeks after trading away his rights to the LA Galaxy earlier this month, and having been described as a fast, ball-winning midfielder who models his game after Yaya Toure, Adjei-Boateng could be exactly the player they are looking for to fill the void left by the departed US international.