"I'm going to try and see what I can do. When I leave here, I'm going to make a call," Jackson joked.
"During the Pro Bowl I was actually telling him, 'Come on man, you know we need you over here.' So I definitely wouldn't mind calling him."
Asomugha, considered by some to be the league's premier shutdown cornerback at age 29, is set to hit the market once a collective bargaining agreement is reached. He gave up only 13 receptions all last season with the Raiders, but Asomugha's $16.8 million option for 2012 voided when he didn't reach certain benchmarks, and Raiders owner Al Davis questioned in January whether that money for Asomugha would be better spent on two or three players.
After Oakland handed cornerback Stanford Routt a three-year, $31.5 million deal in February, it appears likely that Asomugha will leave after eight seasons with the team.
"He has a lot of options, man," said Jackson. "That's a lot of money on his plate …The money he's making is crazy. Hopefully he can take a pay cut and come to the Eagles, and he can see Mike Vick, D-Jackson, (Jeremy) Maclin, (Brent) Celek -- we have a good chance over here, man."
The Associated Press contributed to this report.