The two sides were close to a deal Monday evening with the term of the contract still yet to be agreed upon by the two sides, the source said.
Frolov made $4 million last season and his salary cap hit was $2.9 million.
The talented Frolov would be a welcome addition to a Rangers team that ranked 16th in goals per game last season and has struggled with scoring depth the last couple of seasons.
Frolov's goal total dropped from 32 two seasons ago to 19 last year in part because he fell out of favor with head coach Terry Murray.
But the 28-year-old left-winger will almost certainly get a chance to play with the Rangers' top player, right-winger Marian Gaborik, should the two sides come to terms and those goal totals should bounce back significantly next season.
The 20th overall pick in the 2000 entry draft Frolov has played his entire career in Los Angeles and has twice topped the 30-goal plateau.
The Rangers missed the playoffs last spring for the first time since the lockout, losing to Philadelphia in a shootout on the final day of the regular season.
Earlier this summer it looked as though Frolov, a native of Moscow, would sign a deal with the Kontinental Hockey League before talks heated up with the Rangers.
Scott Burnside covers the NHL for ESPN.com.