Sarah Sanders tweeted that discussions for the visit were already under way.
Earlier Mr Trump rejected a proposal by Mr Putin that Russia be allowed to question US citizens.
The two leaders held a summit in Finland on Monday but few details of what they discussed have emerged.
There has been no word from Russia about a second Trump-Putin meeting.
Controversy has raged over the Helsinki summit, with Mr Trump having to correct his own words from the press conference which followed it.
But on Thursday Mr Trump said the meeting was a "great success" and he was looking forward to their next meeting.
Disclaimer: Comments and opinions on any part of this website are the opinions of blog commenters or anonymous individuals, and do not reflect Strenuous Blog position.