Mr Trump, the likely nominee, and his children were seen leaving the Pence home in Indianapolis.
The businessman is expected to name his vice-presidential pick this week.
Mr Pence endorsed former candidate Senator Ted Cruz in May but said he would support whoever is the Republican nominee.
Mr Trump, his daughter Ivanka Trump and her husband Jared Kushner were seen leaving the mansion.
At a rally in Indiana on Tuesday night, Mr Trump said of Pence: "I don't know whether he's going to be your governor or your vice president, who the hell knows?"