Missouri athletic director Mike Alden flew to Orlando Tuesday morning, while the rest of the Tigers' search committee arrived late Tuesday afternoon, according to the report.
Both parties left in separate cars and, a source familiar with the matter told the Star, Painter will wait another day to decide on his future.
"The ball is in his court," the source told The Star. "Purdue has come up with more money. They don't want to lose him."
Purdue said in a statement that it is committed to keeping Painter.
"Although we will not go into any details at this time, we encourage Matt to stay, through our words and action," Purdue spokesman Tom Schott said Tuesday during a hastily arranged teleconference. "We want Matt to remain a Boilermaker."
The Tigers are looking to replace Mike Anderson, who left Mizzou to take over the Arkansas Razorbacks, where he served as an assistant for 17 years before working his way up the head coaching ladder.
Anderson led Missouri to a 23-11 record this season, but the Tigers were blown out by Cincinnati in the first round of this year's NCAA tournament.
Missouri offered Anderson a $2 million salary to stay in Columbia and, according to the Star, is willing to offer a similar $14 million, seven-year deal to Painter.
Painter is Missouri's top choice to replace Anderson, but Painter is considered a reach because Missouri officials were not convinced he would leave Purdue, the source told Katz.
However, the fact that Alden and Painter have met suggests there is some serious interest, because Alden wanted to be sure a meeting with Painter could result in a hire, according to the source.
Painter, 40, has been named the Big Ten's coach of the year three times and has led the Boilermakers to four straight seasons of 25 or more wins. Purdue (26-8) made it to the third round of this year's NCAA tournament but was knocked out there by Final Four participant VCU.
Purdue officials want to give Painter an opportunity to add to his win total after talking with him Monday night by phone.
"An effort is being made, has been made, was made," Schott said. "What was demonstrated last night is certainly enough of a starting point that he'll understand our desires."
Last year, Purdue rewarded Painter with a new contract through the 2016-17 season. It includes a $1.3 million base salary and up to $1 million in incentives.
Since taking over his alma mater in 2005, Painter has led the Boilermakers to five consecutive NCAA tournaments and back-to-back Sweet 16 appearances.
Former Purdue coach Gene Keady told CBSSports.com that he believes Painter will stay but added the university must show its commitment.
"Matt wants a situation where he will be able to make a run for a national championship," Keady said. "The administration here has to step up and help him."
Information from ESPN.com senior college basketball writer Andy Katz and The Associated Press was used in this report.