Rodgers sparked a reaction from Rangers boss Philippe Clement as he looked towards Saturday’s derby clash between their teams.
Arsenal need a favour from another club in the final week of the season if they are to deny Man City a fourth successive Premier League crown.
The injury-hit Red Devils suffered a club-record 13th defeat of a Premier League season on Monday night with the 4-0 hammering at Crystal Palace.
Chairman Todd Boehly talked up his side’s progression under Pochettino earlier this week after Chelsea leapfrogged Manchester United into seventh.