Donald Trump Jr, Jared Kushner and Paul Manafort are accused of having links with Russian officials.
Mr Trump and his allies have denied any collusion.
Meanwhile, Mr Trump said he would not have named Jeff Sessions had he known he would recuse himself from the probe.
In an interview with the New York Times, Mr Trump called the attorney general's decision "very unfair".
"Sessions should have never recused himself, and if he was going to recuse himself, he should have told me before he took the job and I would have picked somebody else," Mr Trump said.