The Republic of Ireland international striker impressed whilst out on loan at MK Dons last season, scoring 10 goals in 47 across all competitions.
The 20-year-old former Ipswich Town and Millwall loanee is highly rated by Tottenham Hotspur, who are said to be keen to loan the striker out again next season.
And former Sunderland player Elliott has reckons Parrott and Sunderland could be a smart move by both parties.
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"He's had that full season at League One and I think he's a better player now than League One," he told the RTÉ Soccer Podcast.
"I know people say he didn't score loads of goals in League One but the way he plays, he was always involved in goals and he started to score a few more towards the end of the season - some really good goals.
"But for him to keep improving, he needs to move himself up a level. I think somewhere like Sunderland - they need a couple of strikers - they've got Ross Stewart there at the moment but he could do with a little help in there.
"I think if Troy Parrott came to Sunderland, I think he'd embrace playing for a club like that with the big crowds, the atmosphere at the games and that feeling of doing well there and thriving there.
"He looks like the type of player that thrives on playing on the big occasion and I think it could be a really good move."