It is understood that fellow Championship side Huddersfield Town have also had an offer turned down for the 21-year-old.
Neither side have matched Wimbledon’s valuation this summer and thus will need to make another approach if they are to have a chance of winning the race for Rudoni’s signature.
In total, it is believed that four clubs have now made bids in the current transfer window.
Rudoni is currently training with Wimbledon who are preparing for life in League Two following their relegation to this division earlier this year.
A separate report from the South London Press earlier this month revealed that Sunderland, Huddersfield and Bristol City were unsuccessful with their initial bids for the midfielder.
These offers would have exceeded £1m if add-ons were triggered in the future.
A shining light in what otherwise was a season to forget for Wimbledon, Rudoni produced a host of promising performances for the club in League One.
Sunderland quiz: Does the Stadium of Light have a bigger or smaller capacity than these 20 stadiums?
Having now had two offers rejected by Wimbledon, it will be interesting to see whether Sunderland continue this particular pursuit.
Whereas Rudoni has yet to feature in the Championship during his career, there is no doubt that he could potentially thrive in a higher division in the not-too-distant future.
As well offering an attacking threat in the previous term, Rudoni also made 1.7 tackles and 1.1 clearances per game in the third-tier as he averaged a WhoScored match rating of 6.90 at this level.
Providing that Sunderland are able to reach a breakthrough in negotiations with Wimbledon, Rudoni’s arrival at the Stadium of Light may force the likes of Corry Evans, Elliot Embleton and Dan Neil to step up their performance levels.
This in turn could have a positive impact on the club’s fortunes in the Championship later this year.