Shimkus's staff said Wednesday that his campaign includes meeting with Republican members to make his case.
"Shimkus has been meeting with Steering Committee members all week, including up to the House GOP organizational meeting this afternoon," his office said in a statement on Wednesday.
"He also wrote all members-elect regarding his interest in serving as chairman. He is very well prepared to run the committee if given the opportunity by his colleagues," the statement said.
Term limits could disqualify Barton, the committee's ranking member, unless he obtains a waiver from party rules.
Barton, however, says the rules are ambiguous and need not prevent him from leading one of the most powerful House committees, which oversees energy, health, and telecom policy, among other issues.
Shimkus agreed with Barton's interpretation on Wednesday.
"Shimkus has always supported members serving six years as chairman and a separate six years as a ranking member. He feels the waiver rule is unclear and needs to be addressed," said a statement from his staff.
The competition for the Energy and Commerce gavel has heated up since the election, with Rep. Fred Upton (R-Mich.) seen as a frontrunner.
Shimkus and Rep. Cliff Stearns (Fla.) have each tossed their hat in the ring if Barton cannot take the gavel, banking on the possibility that they could be viewed as more reliably conservative than Upton.
The conventional wisdom this week is that Barton seems unlikely to obtain a waiver. His aggressive bid for the gavel and his alleged work to undermine Republican competitors has complicated his already tense relationship with the leadership, according to industry sources.
Also working against the odds: Barton's remarks earlier this year that were perceived as an apology to BP after the oil spill. His comments created a public relations debacle for his party.