Washington (CNN) Democratic presidential candidate Julián Castro said Sunday that should former Starbucks CEO Howard Schultz run for president as an independent, he would give President Donald Trump the "best hope of getting re-elected."

Last week, CNN reported that two people familiar with Schultz's thinking said the businessman is exploring a 2020 presidential run as an independent . After he stepped down from his position at Starbucks last year, Schultz said at the time that he may consider a White House bid.

"I have a concern that if he did run, that essentially, it would provide Donald Trump with his best hope of getting re-elected," Castro, the former secretary of Housing and Urban Development, told CNN's Jake Tapper on "State of the Union."

"Just the other day, there was a fairly comprehensive poll taken that showed, essentially, right now, that the President has a ceiling of about 41% or 42% in terms of support for him no matter which Democratic candidate they polled against him," Castro said. "So his only hope -- if things stayed the same, and that's a big if -- is essentially to get somebody else, a third party, to siphon off those votes. And I don't think that that would be in the best interest of our county."

"I would suggest to Mr. Schultz to truly think about the negative impact that that might make," Castro added.

Read More