Michael Fabricant, Conservative MP for Lichfield, has asked for the probe after Marcus Rashford, Bukayo Saka and Jadon Sancho were targeted with racist abuse after missing penalties in Sunday's Euro 2020 final loss to Italy.
He suggested that much of the abuse may not be "home grown" and questioned whether overseas fans or foreign states may be "attempting to destabilise our society".
Mr Fabricant was responding to a tweet calling on Boris Johnson to provide evidence of "which accounts were England fans".
He has tabled a written parliamentary question to Home Secretary Priti Patel asking "if her department will commission an investigation through its agencies what proportion of the racist tweets directed at three players in the recent UEFA finals match originated in the United Kingdom".
He also called for the Home Secretary to issue a report following the investigation.
Mr Fabricant told the Express & Star: “It’s been said that data from the last two seasons of football show around 70 per cent of racist abuse on twitter and other social media originates from overseas.
"I don’t know if this is just wishful thinking or whether there is a real underlying and nasty race problem now in the UK. But I hope that Government agencies like GCHQ can get to the bottom of this.
“Is it overseas fans or foreign states attempting to destabilise our society? I hope it is this and that this abuse is not home grown. But the Home Secretary is responsible for our law and order and so I have asked her to find out.”
Mr Johnson was due to discuss the issue of online abuse in a meeting with internet companies in Downing Street yesterday.
It comes after Aston Villa and England star Tyrone Mings criticised Ms Patel over her suggestion before the tournament that the players' decision to take the knee was "gesture politics".
Responding to the Home Secretary's condemnation of racism against players, he tweeted: "You don’t get to stoke the fire at the beginning of the tournament by labelling our anti-racism message as ‘Gesture Politics’ & then pretend to be disgusted when the very thing we’re campaigning against, happens."