It has been claimed that Aston Villa, Wolverhampton Wanderers, Derby County, Sheffield Wednesday and Fulham are all keen on the 24-year-old, and Clough has acknowledged that a transfer could take place.
He told BBC Radio Derby: "We're realistic. If an offer comes in — and it's the right offer — and Jackson feels that it's a step up in progress for him, then it's very difficult for us to stand in his way."
Irvine only moved to the Staffordshire outfit last season after leaving Ross County, but 10 goals from 42 Championship appearances has led to him becoming a target for several teams in the second tier.
He played a key role as Burton retained their status in the division after gaining promotion from League One during the 2015-16 campaign.