The Sun says FA chiefs will only consider his position if he is convicted of "a serious criminal offence."
The Liverpool captain was charged with assault and affray in the early hours of this morning.
Police launched their probe after a DJ was taken to hospital for treatment on facial injuries following a bar brawl early yesterday.
Gerrard, 28, was one of six men arrested after the fight in a Southport nightspot.
Any case against Gerrard is unlikely to come to court before England's next game away to Spain on February 11.
And the FA will not get involved in the matter while police inquiries are on-going.
An FA spokesman said: "No one knows the full facts so we are not even discussing this matter.
"No player is banned from representing England while they are the subject of a police inquiry.
"That position would only change in the case of a conviction for a serious criminal offence. Then the case would be considered on its individual merits."