Jenkins' refusal to admit any wrongdoing to Giants head coach Pat Shurmur is what reportedly led to the team parting ways with the 31-year-old cornerback.
Jenkins reacted to being released from the 2-11 Giants by saying it was the "best news ever."
49ers general manager John Lynch joined KNBR on Friday morning for his regularly-scheduled interview and was asked about the possibility of bringing in Jenkins.
"We look into everything, any time a player comes across the wire," Lynch responded on the "Murph and Mac" show. "Guys are doing that right now, but we do like our cornerback group.
"When you talk about young kids like (Emmanuel) Moseley and (Ahkello) Witherspoon, and then Richard Sherman; this week, we brought in Dontae Johnson, so we like our group.
"But absolutely, we always take a look and see what's out there. If things ever make sense, and we feel it can improve our chances to win, we'll jump on it. I'm sure someone's looking at him right now. I probably will when we hang up."
Jenkins has 54 tackles this season and is tied for fourth in the NFL with four interceptions.
You can listen to the entire conversation with Lynch below.
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