The Rams recently 'swiftly rejected' a bid - thought to be around £1m - from Wigan Athletic for the 25-year-old defender, who has 12 months to run on his existing contract.
While Clough hopes the defender will agree a new deal with the club, he expects the situation to be sorted out one way or the other before the start of the season.
He told the Derby Evening Telegraph: "They (Wigan) may be pursuing one or two other targets, which is fine by us.
"We sat down with John at the end of last season and he was relaxed about the situation.
"The type of character John is, there are no worries about what he is going to give us on the pitch whether his contract has a year, a month or a week to run.
"We have just got to protect our investment as a club. We are talking with John and we hope he will be with us.
"I expect this to be sorted before the start of the season."
While the Rams have been linked with Liverpool's 20-year-old right-back Jon Flanagan should Brayford be sold, Clough says Kieron Freeman would get his chance.
"If John did go, we would put Kieron Freeman in," Clough insisted.
"Valentin Gjokaj filled in at right-back last season, and did not let us down at all. Nor did Ben Davies when he played the position.
"If you want the strongest possible squad, then John Brayford plays and Kieron Freeman covers at right-back and left-back.
"That would be the ideal scenario."