"According to a league source, the 49ers were seeking a mid-round pick for their quarterbacks," wrote Barrows within a recent roster breakdown.
General manager John Lynch told reporters via a conference call on Saturday that there were discussions with teams, but nothing concrete materialized because no one was willing to meet the 49ers' asking price.
"In the last week, there was a lot of interest, a lot of conversations," Lynch said. "That position to us is one that you just set a price on, and you stay firm on it. While we had discussions, we never deviated from what that price was for us, and nobody ever met it, so we were happy to carry the three in.
"We believe that's a great position to be in a position of strength, and we feel from our starter from Jimmy on down to the other two that it is a great position of strength. Not that we weren't open to it, but a certain price had to be met, and it wasn't. So we go in happily with these three."
Unless something happens in the next week, the 49ers will enter the regular season with three quarterbacks on the roster for the first time since Lynch and head coach Kyle Shanahan took control of the team. Beathard has been a part of each of those three initial rosters.
San Francisco will enter Week 1 with Mullens and Beathard as the backups to starter Jimmy Garoppolo. A decision on which of the two will be the primary backup has already been made, said Lynch, but the quarterbacks will not be informed of that decision until Monday.