In a press release posted on their site, Slavia revealed that all of the details for the transfer have been agreed.
Krastev, 18, will sign his contract next week and then a final announcement will come.
It is believed City are paying around €2m for Krastev, who they view as an investment for the future.
The Bulgarian club also asked the local press ‘not to bother’ the young player, who is focusing on upcoming matches.
Krastev is a Bulgarian under-19 international and has made seven appearances in Bulgaria’s efbet Liga this season.
His main position is central midfield in a deep-lying playmaker role, but he can also play further up the pitch.