Horsfield, 34, is without a club after being released by Sheffield United at the end of last season.
Downing told the Robins' official website: "Geoff's just training with us at the moment. He hasn't done a lot in pre-season but we're having a look at him and he's having a look at us.
"When fully-fit he's a very good player so we're going to see how we get on with it."
Bristol City trainee Callum Hart is also currently on trial at Whaddon Road, although Downing has decided not to offer a permanent contract to the former QPR and Cardiff City midfielder Richard Langley.