A source told ESPN that all three were identified as high-risk close contacts to an outside practitioner who tested positive. The Browns are hopeful that all three will be available for Sunday's game against the Philadelphia Eagles if they continue to test negative this week.
Coach Kevin Stefanski said Kendall Lamm would start at right tackle if Conklin is unable to play.
Though the practice facility remains open, Cleveland is in the NFL's intensive protocol and holding all meetings remotely.
Fullback Andy Janovich was placed on the reserve/COVID-19 list Monday. Reserve offensive lineman Chris Hubbard was put on the list last week.
Stefanski said defensive end Myles Garrett would not practice Wednesday after being sent home for feeling sick. Garrett leads the NFL with 9.5 sacks.