Both sides sit on one point in Group A after two matches.
Real drew 2-2 with Club Brugge in their last European outing, while Galatasaray tied 0-0 with the Belgian outfit in September.
Date: Tuesday, October 22
Time: 8 p.m. BST/3 p.m. ET
TV: BT Sport ESPN (UK)
Odds: Galatasaray (23-5), Draw (31-10), Real Madrid (59-100)
Odds courtesy of Caesars
Real come into the match on the back of their first La Liga defeat of the season, after losing 1-0 to Real Mallorca on Saturday.
Fox Sports' James Dodd would not be surprised if they lost on Tuesday, too:
In the Champions League, they were beaten 3-0 at Paris Saint-Germain despite the French side playing without Kylian Mbappe, Neymar or Edinson Cavani.
Real have named Kroos and Hazard in their 21-man squad for Tuesday's game, and they'll need the latter in particular to perform.
Fellow summer signing Luka Jovic was handed a start on Saturday, but as OptaJose illustrated, he struggled to have an impact on the game:
Tom Allnutt of the Agence France-Presse put his difficult start at the Santiago Bernabeu in perspective:
Until the striker is able to find his feet at his new club, Madrid need the likes of Hazard to pick up the slack in the final third.
At the other end, Real have shipped five goals in their last three matches, so they'll be thankful their opponents have had troubles scoring this season.
Despite bringing in striker Radamel Falcao in the summer, Galatasaray have only scored nine times in their eight league matches this season, and they've failed to find the net in their first two Champions League games.
Real are yet to convince, though, so it's far from guaranteed they'll have an easy time on Tuesday even amid the Turkish side's attacking struggles.
Los Blancos need to take three points if they are to get their Champions League campaign back on track, but they will have to play markedly better than they have recently to do so.