The Cobblers were approached by an unnamed club on Tuesday morning regarding Jacobs, whose contract expires in the summer.
The 20-year-old has been watched by several League One and Championship clubs this season and Cardoza expects the interest in Jacobs to escalate.
"We turned down an offer for Michael this morning," Cardoza told the Northampton Chronicle. "We know a lot of offers are going to come in for him but he will have the final say in the end.
"I can't say how much was offered this morning but it was not enough. We are talking about Championship clubs but the season hasn't finished yet and I am sure that interest will grow in the next few weeks."
Because Jacobs is under the age of 24, Town would be entitled to a tribunal-set compensation payment if he was to leave Sixfields.