Budgett, who missed the Blues' 9-9 draw against former Celtic League champions Leinster in the opening round of the season, had originally been ruled out for six weeks after injuring his neck in a pre-season game against Worcester.
But he has been told that he does not need to undergo surgery and will resume full contact training in time for the derby clash with the Dragons.
'It's a real relief to be told I don't need an operation as that would have set me back perhaps months,' said the 12-times capped lock.
'I've had plenty of injury problems over recent years and I'm just desperate to get a run of games under my belt. Hopefully this won't hold me back too much.' said the former Bridgend and Ebbw Vale man.