The deal can be formally agreed to in principle Monday and finalized after the NBA draft on Wednesday night.
As part of the trade, the Lakers are preparing to send the player they select with the 28th overall pick and guard Danny Green to the Thunder, sources said.
Los Angeles cannot outright send the draft pick to Oklahoma City because there is a rule that restricts teams from trading first-round picks in consecutive years. Los Angeles sent the No. 4 overall pick in the 2019 draft to the New Orleans Pelicans as part of the Anthony Davis trade. The Thunder already own the 25th pick in Wednesday's draft.
Schroder, 27, has been one of the most sought-after guards in the trade market, and he fortifies a Lakers backcourt that potentially could lose veteran guards Rajon Rondo and Avery Bradley in free agency.
Schroder has one year and $15.5 million left on his contract and would be acquired with the intention of eventually signing him to a new contract to remain with the defending NBA champions, sources said.
Oklahoma City acquired Schroder in 2018 from the Hawks in exchange for Carmelo Anthony and a lottery-protected 2022 first-round pick. If the pick doesn't convey, it turns into two second-rounders, which is an increasingly likely scenario given the Thunder's rebuilding plan beginning in action.
Schroder finished runner-up for Sixth Man of the Year last season, becoming a key component to one of the best combinations in the NBA, a three-point-guard lineup alongside Chris Paul and Shai Gilgeous-Alexander. Though he excelled in his role, averaging 18.9 points and 4.0 assists, Schroder was never shy about his desire to return to the starting lineup and the Lakers are poised to give him that opportunity.
ESPN's Royce Young contributed to this report.