However, the Raiders are in a "distant" third place and don't appear close to landing the former No. 1 pick, sources told Reed and Tafur.
The Seattle Seahawks, Tennessee Titans, and Cleveland Browns were previously reported to have made offers this offseason, with the Browns presenting the most lucrative deal.
Raiders head coach Jon Gruden is a big fan of Clowney, however, and would like to increase the bid, according to Cecil Lammey of 1043 The Fan.
Clowney, 27, was expected to be one of the first high-profile free agents to sign this offseason. However, his market didn't turn out as expected, and he lowered his asking price from $20 million annually to around $17 million to $18 million.
The three-time Pro Bowler played one season in Seattle after being traded from the Houston Texans, racking up 31 tackles, three sacks, four forced fumbles, and one interception through 13 contests. Clowney has played a full 16 games only once in six NFL campaigns.
Las Vegas was a bottom-10 team in sacks last year with 32 and pressured opposing quarterbacks in less than 20% of their dropbacks.
The Raiders currently have just $8.28 million in cap space, according to Over The Cap.