A contract extension appears to be higher on their list of priorities.
"Right now, I think we're more into OTAs and let's see if we can get something done by the end of this thing," Rams general manager Les Snead told reporters during a news conference at Tuesday's start to the Rams' voluntary veteran minicamp. "That's where we're at right now."
Johnson, who replaced Janoris Jenkins as the team's primary corner last season, is playing under his second consecutive franchise tag, one that will guarantee him a one-year, $16.74 million contract for 2017.
Signing Johnson to an extension would reduce his cap hit for 2017, because he may sacrifice immediate dollars for long-term security and because the Rams would be able to prorate his signing bonus through the length of his new deal.
That would then give them more flexibility to extend several other defensive players who are eligible for free agency next offseason, a daunting list that also includes linebacker Alec Ogletree, strong safety Maurice Alexander, potential free safety Lamarcus Joyner and cornerback E.J. Gaines.
It would also lock up their best defensive back, Johnson, who compiled 15 interceptions from 2012 to 2015.
The 27-year-old has been with the team since the start of its offseason program.
"I'm glad to be a Ram, point-blank," Johnson, the Rams' third-round pick in 2012, told reporters after practice. "Coming out here, it's a privilege to play football. I'm glad I'm on the team and I'm with the Rams."
Asked about remaining with the Rams long term, Johnson said: "Of course. I love these guys. I'm here because I love my teammates. I don't want to leave. Hopefully we get a long-term deal."
The Rams were unable to get an extension done with Johnson last offseason, a time when Jenkins and free safety Rodney McLeod both departed via free agency.
Earlier this offseason, Snead indicated the team preferred to get through the offseason program before revisiting extension talks with Johnson in order to first see if he would be a fit under new defensive coordinator Wade Phillips.
The Rams also were shopping Johnson to other teams at the start of free agency, hoping to relieve some cap space while potentially receiving a higher selection for the 2017 draft in which they won't have a first-round pick. But a free-agent crop led by A.J. Bouye and Stephon Gilmore prompted teams to go elsewhere. And the presence of Richard Sherman and Malcolm Butler on the trading block pretty much spoiled any chances of a deal.
Johnson, ranked 25th among corners by Pro Football Focus last year, took it in stride.
"This whole month and a half, I've been controlling what I can control, and that's working out," Johnson said when asked about trade rumors. "I'm not worried about that. I'll know when it comes. And when it comes, I'll handle it."
A price gauge for Johnson's potential extension might have come with the one recently given to Desmond Trufant, who signed a five-year, $69 million deal with the Atlanta Falcons that ranks fourth among corners in average annual value.
The Rams have until July 15 to agree to a long-term deal with Johnson, and they sound a lot more open to it in late April than they did during the combine in early March.
New head coach Sean McVay, who has spent some time with the defensive backs over the last couple of weeks, praised Johnson's work ethic and attention to detail.
"He's a leader, and that's what you expect from a top-caliber corner like he is," McVay said. "We're fortunate to have him."