Los Blancos are in a dismal run of form, leaving former Arsenal boss Arsene Wenger also in the frame for the job.
Madrid's winless streak stretched to four matches on Saturday with defeat away to Alaves.
This is their third defeat in this poor run, leaving former Spain boss Lopetugui under huge pressure at the Bernabeu.
The bookies have Pochettino as second favourite at 3/1 to arrive as boss, behind Guti who is 2/1 in the market.
Alex Apati of Ladbrokes said: "Things haven't exactly gone according to plan for Madrid so far this season and with pressure on Lopetegui's shoulders intensifying, we reckon the La Liga giants could turn to Poch."
Wenger is 16/1 as he remains out of work since he left Arsenal last summer.
The former Gunners boss refused to rule out retirement as he continues to review his options.
The Frenchman also trails Antonio Conte and Laurent Blanc in the bookies' eye.
While Wenger is the same price as Juventus boss Massimiliano Allegri and Germany's national coach Joachim Lowe.
Ladbrokes: Next Real Madrid manager
Guti – 2/1
M.Pochettino – 3/1
A.Conte – 5/1
L.Blanc – 6/1
A.Wenger – 16/1
M.Allegri – 16/1
J.Low – 16/1
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