UEFA has proposed new, tougher anti-racism sanctions from next season, including a partial closure of stadiums for a first incident of racist abuse by fans — rather than just a fine — and a full closure for a second offence.
FIFA President Sepp Blatter, meanwhile, has backtracked on calls for teams to be punished with relegation after serious racist abuse over fears fans would deliberately provoke incidents.
Hodgson, who has also coached in Sweden, Denmark, Norway, Switzerland and Italy, appears to share Blatter's concerns, highlighting the danger of far-right extremists.
"The one thing that concerns you a little bit is what happens at the stadium, it's very difficult to control every element," Hodgson said at the SoccerEx conference in Manchester. "One does fear sabotage, with groups of people coming in who have nothing to do with football and who are perhaps of a Nazi persuasion and who could cause an awful lot of problems."
Hodgson didn't specify which countries he thought might be afflicted by the trouble.
FIFA's punishments only apply to its international competitions, and UEFA can only enforce its sanctions in European fixtures.
UEFA, though, is asking its 53 members at next month's congress to adopt the proposed tougher anti-racism sanctions that include a 10-match minimum ban for players found guilty of abuse.
The English Football Association, which is hosting the congress, isn't sure if it wants to emulate European football's governing body.
"We wouldn't necessarily get to the same solution as UEFA," FA chairman David Bernstein said. "It's not a race to be first past the post, we'll do it at our own pace in our own way.
"I'm delighted UEFA have come up with this strong penalty and I fully support them doing it. But English football must come to its own decision in its own time, which will be very soon."
In England in recent years, Liverpool striker Luis Suarez received an eight-match ban for racially abusing an opponent and Chelsea captain John Terry was suspended for four matches.
Another turbulent episode for English football last week centred on the apparent past fascist allegiances of Paolo Di Canio, whose appointment as Sunderland manager provoked outrage.
It took three days for Di Canio to insist that he does "not support the ideology of fascism."
"Paolo Di Canio certainly appears to have retracted some of his previous statements and there have been some moves in the right direction," Bernstein said.
"We deplore any association with fascism and any association with racism," Bernstein added. "And hopefully Paolo Di Canio is moving the agenda in the right direction and that issue will be put to bed."
Rob Harris can be reached at http://twitter.com/RobHarris