A source with knowledge of the situation told Pro Football Talk that the "disagreement" has existed since 2015.
Cousins has been the focus of trade talks, an extension and playing on the franchise tag for months. The deadline for signing Cousins to a long-term deal is on Tuesday.
According to the Pro Football Talk report, the discrepancy began in 2015, after Cousins and Griffin both had more than 200 pass attempts during the 2014 season.
Cousins completed 61.8 percent of his throws for 1,710 yards, 10 scores and nine interceptions while Griffin completed 68.7 percent of his passes for 1,694 yards, four touchdowns and six interceptions. Griffin started seven games while Cousins started five contests.
Some within the Redskins' organization weren't ready to let Griffin go in favor of Cousins due to his high draft pick investment, according to Pro Football Talk.
The next season, the Redskins unleashed Cousins. He completed a league-best 69.8 percent of his throws for 4,166 yards, 29 scores and 11 interceptions while starting all 16 games and posting a 9-7 record.
Washington released Griffin before the 2016 season.
Cousins made $19.9 million last season and is due $23.94 million on the franchise tag this season. He could make more than $34 million next season if the Redskins decide to give him the franchise tag again.
Bleacher Report reported Friday that McCloughan wanted to pay Cousins about $12 million annually in a long term deal in 2015. When discussions moved past $20 million annually in 2016, McCloughan became "uncomfortable."
Last summer, the Redskins offered Cousins a deal for $16 million annually with $24 million in guarantees, according to NFL.com.
Cousins now has himself in position for a big payday, from the Redskins or elsewhere. Still, some scouts don't believe he is a "difference maker."
"He is what he is," an NFC pro scouting director told NFL.com. "He is a solid starter capable of winning games when surrounded by supreme talent in that system, but I don't think he is a difference maker...would have a tough time paying $25 million for a guy that I don't believe can carry us to the Super Bowl."
By not signing a long-term deal, Cousins stands to make about $44 million over two years. He could earn up to $78 million in three years if he plays under the franchise tag in 2018.
Two NFL general managers told Bleacher Report that some team will use a "huge roster bonus" on Cousins next offseason to make it difficult for the Redskins to match on the transition tag if the team chooses not to sign him long-term.
NFL Network reported that both Cousins and the Redskins are OK with the quarterback playing under the franchise tag this season. Sources told NFL Network that there is a "strong indication" that Cousins plays out the season under the tag.
After signing his $125 million deal this offseason, Derek Carr is currently the league's highest-paid player. Cousins' 2017 salary ranks No. 4 among quarterbacks, trailing Carr, Luck and the New Orleans Saints' Drew Brees, according to OverTheCap.com.
Detroit Lions quarterback Matthew Stafford is also eyeing a huge contract extension as he is playing out the final year of his five-year, $76.5 million contract. The Lions have been working on an extension with the Pro Bowl gunslinger this offseason, which should place him among the highest paid quarterbacks in the league.