Coe, president of world athletics, must answer questions raised in a BBC documentary, says Jesse Norman, chair of the House of Commons' Culture, Media and Sport select committee.
"I'd say it's almost certain we'll want to have Lord Coe back in front of the committee," said Norman.
Russia was suspended from international athletics in November last year.
Coe, who won Olympic 1500m gold in 1980 and 1984, denies any wrongdoing.
The BBC's Panorama programme claimed Coe was aware of details of a Russian doping corruption case four months before it became public and may have misled MPs at a Culture, Media and Sport committee meeting last year.
"I don't want to get too far ahead of where the committee is going to be, but these are very serious matters," Norman told the Radio 4's Today programme.
Lord Coe, 59, became president of the International Association of Athletics Federations in August last year, succeeding Senegal's Lamine Diack.
Lord Coe faces "very, very disturbing" allegations about his knowledge of Russia's doping problems, says a UK MP.