Pence called Hawley over the weekend to encourage him to enter the race, a spokesman for Hawley confirmed to CNN. The vice president joined a chorus of prominent Missouri Republicans who have been publicly pushing Hawley to run.
"Josh spoke to Vice President Pence this weekend and has been getting a great deal of encouragement to run," spokesman Scott Paradise said in a statement. "He is giving the race serious consideration. Josh has also received calls from others interested in running and he is letting them know of his decision to consider the race."
A source familiar with Hawley's thinking said there was a "full-court press" over the weekend to get Hawley, who was elected the state's attorney general in November, to enter the race.
"I do think when you've got the vice president calling you on top of the who's who of the Missouri political network calling you, it's gonna make it tough on him to say no," the source added.
The contest in Missouri could be one of 2018's most high-profile races and has attracted the attention of a number veteran Show Me State politicians. Earlier this month, Rep. Ann Wagner, a longtime Republican and prolific fundraiser, opted not to challenge McCaskill
and instead run for re-election to her suburban St. Louis seat.
McCaskill has held Missouri's Senate seat since 2007 after defeating Republican Sen. Jim Talent in a contentious race. She was viewed as one of the Senate's most vulnerable incumbents in 2012, but handily won re-election over Rep. Todd Akin, whose comments about "legitimate rape" rocked his campaign
This year though, Republicans see fresh opportunity in a state that President Donald Trump won by 19 points.
"Trump did very, very well here, but Josh led the ticket," former Missouri Sen. Jack Danforth, a Republican, told CNN.
Danforth is one of a number of prominent Missouri Republicans, including former Lt. Gov. Peter Kinder and David Humphreys, a major GOP donor from southwest Missouri, who in April signed a public letter urging Hawley to jump into the race, calling him the "strongest candidate for Missouri's Senate seat."
Sam Fox, the St. Louis businessman and former US Ambassador to Belgium, has also sent a letter to Republican donors asking them to withhold their support from other potential candidates until Hawley makes a decision about the race.
Hawley has yet to say whether he plans to enter the race.
"I think it would clear the field," said Danforth of a potential Hawley bid.
Danforth, a moderate Republican who represented Missouri in the Senate from 1976-1995, described Hawley, whom he has known since he was a Yale Law student, as a "once in a generation person in politics." He compared Hawley to Daniel Patrick Moynihan, the four-term United States senator and Harvard professor from New York, citing Hawley's legal experience and a book he authored about Theodore Roosevelt as examples of his "breadth and depth."
Hawley, a former law professor at the University of Missouri, won election to the attorney general's office in November after a bruising and costly primary contest with a veteran Republican lawmaker Kurt Schaefer. He later defeated Democrat Teresa Hensley in the general election, making him the first Republican to hold the office in more than 20 years.
Missouri's Democrats are already casting Hawley as an opportunist. Stephen Webber, the chairman of Missouri's Democratic Party and a former state representative, blasted Hawley as hypocritical for potentially considering a run for the Senate within his first term as attorney general.
"He literally ran an ad that had politicians climbing ladders and was critical of career politicians and that was less than a year ago," Webber told CNN. "It would be a telltale sign of a typical politician if he decides to run for office after less than a year after winning office."
In the ad, Hawley says that Missouri's state capital of Jefferson City is "full of career politicians just climbing the ladder, using one office to get another."
"I'm Josh Hawley, I think you deserve better," Hawley says in the ad.
A spokesman for Hawley did not say when Hawley was expected to make a final decision, but a source familiar with Hawley's thinking said a decision could come at the beginning of August.
Hawley attended high school in Kansas City before studying at Yale Law School. He clerked for Chief Justice John Roberts and has served as senior counsel for the Becket Fund for Religious Liberty.
Hawley is not on his own in considering a run. A number of other Missouri Republicans are also considering mounting challenges to McCaskill. Reps. Vicky Hartzler, Blaine Luetkemeyer and Missouri State Rep. Paul Curtman are all also potential McCaskill challengers. The St. Louis Post-Dispatch reported last week
that Curtman, who has served in the state legislature since 2010, could announce an exploratory committee for his Senate bid as early as this week.