According to Sky Sports, personal terms have been agreed and the move to Cologne is expected to be finalised in the coming days, with several other clubs from England and across Europe having made enquiries for the 18-year-old.
Tottenham's hierarchy see Köln as offering the best environment for his continued development, despite earlier interest from Middlesbrough, Rangers and Hamburg among others.
Moore spent last season on loan at Rangers, where he impressed despite his young age, scoring seven goals and providing four assists in 47 appearances across all competitions and winning the Scottish Premiership's Young Player of the Year award.
He also holds the record as England's youngest-ever scorer in a major European competition, having netted for Spurs in the Europa League against Elfsborg at 17 years and 172 days old, beating a mark set by Jimmy Greaves in 1957.
Borussia Dortmund had also registered interest earlier in the window but wanted the option of a permanent transfer included in any loan, a condition Tottenham rejected, leaving Köln to move into pole position for a player who has already been capped at England Under-19 level.
Moore made his senior Tottenham debut as a 16-year-old and became the youngest player to start a Premier League match for the club since Stephen Carr in 1993, underlining the level of expectation that follows him despite his tender age.
Köln have shown a willingness to work with young English talent before, with Reigan Heskey and Jahmai Simpson-Pusey both already on their books, and see Moore as a similarly promising addition capable of gaining regular first-team football in the Bundesliga while continuing to progress as part of Tottenham's long-term plans.