Durbin spokesman Joe Shoemaker said Durbin will give up his chairmanship of the Senate subcommittee to Specter, who recently left the Republican Party to become a Democrat, CNN said.
The Crime and Drugs panel is a subcommittee of the Senate Judiciary Committee. Specter was the ranking Republican member of that committee before he changed party affiliation.
Durbin's decision comes in the wake of Senate Democrats wiping out the Pennsylvania politician's decades of Senate seniority.
Shoemaker said the Crime and Drugs Subcommittee is a powerful position in Washington as it apparently oversees nearly 60 percent of Department of Justice operations.
An unidentified Democratic Party source told CNN the decision to give Specter the chairmanship of the subcommittee was intended to help him get re-elected and to avoid any conflict as the Judiciary Committee considers a Supreme Court nomination.
"The last thing we want is a disgruntled Democrat at the end of the dais," the source said.