The goalkeeper missed the trip to Norwich and tour to South Africa with the injury, that was troubling him last season, but reveals that it is not cause for undue concern.
"To be honest, it has improved quite a lot over the last few days," said Sully. "I'm going to leave it another couple of days over the weekend and hopefully start again on Monday.
"It was nothing serious, just something that was niggling me at the back end of last season and didn't really settle down in the summer as I would have hoped.
"I had it scanned and looked at and they found a couple of little problems. Nothing major, I had a injection that seems to have settled things down.
"I want it to be 100 per cent before I start. We're so close to the season now, if it breaks down you are into missing Premiership games.
"It was unfortunate to miss the South Africa trip, but I needed to get it right."
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Neil Sullivan reports good progress on his shoulder problem and hopes to be back in training next week.