Appleton is one of the leading contenders for the permanent job, having also been linked to the managerial position at West Bromwich Albion.
"Look, Sunderland is a big club and it's always nice to be linked with clubs like that," Appleton told BBC Radio 5 live.
"Sunderland is certainly a big job and it's nice to be mentioned as a potential candidate. But ultimately, from my point of view, I'll be focusing everything I do on Leicester City until I'm told otherwise.
"Every manager would like that backing [of patience], but in today's game it's very rare you're given much time. But to build a club and a style and a relationship with fans, you are only going to get that with time. Ultimately at Sunderland for too long that hasn't been the case."
Sunderland have now suffered back-to-back relegations and will play the 2018-19 season in League One.