Reports claim a £3million offer has been lodged.
Southgate confirmed his intention to replace recently departed Luke Young, but did not want to comment on any interest in taking Hoyte to the Riverside.
"I am not talking about players who belong to other clubs," Southgate told the Evening Gazette.
He added: "What is clear is there are a lot of right-backs currently available. We have had a lot of calls as a result of Luke moving on.
"We have a good idea of what we would like and we are confident we can do some business before the start of the season."