Miami has four other tight ends in camp and added two more on Monday when the team signed tight ends Sal Cannella and Kalif Jackson.
They were put on the list as close contacts, sources told ESPN's Adam Schefter on Sunday, after Dolphins co-offensive coordinator and tight ends coach George Godsey, who has been vaccinated, tested positive for COVID-19 and was sent home.
Co-offensive coordinator Eric Studesville will run the Dolphins' offense in Godsey's absence.
The Dolphins have had four training camp practices and were off Sunday.
Gesicki's 703 yards receiving in 2020 ranked fourth among NFL tight ends and were the second most in a season by a Dolphins tight end.
The Associated Press contributed to this report.