The 33-year-old was not named in the starting lineup for the Ravens during the regular season, but had an increased role during the the playoffs.
Michael George told the Baltimore Sun: "Bryant would want to come back. He likes it there. He likes the situation, the way it is now. He's a free agent, so it's up to the Ravens what happens next, obviously.
"The intention is to see what the market says. If the Ravens want to do something, we're definitely open to that. Obviously, it has to be [the] right numbers for both sides.
"Whatever happens with the Ravens, it depends on them and whatever discussions are held before free agency. There are a lot of teams with needs at tackle, and there are maybe a half-dozen good ones in free agency."
McKinnie has played for the Ravens for two season, having started his NFL career with the Minnesota Vikings in 2002.