Democratic presidential front-runner Hillary ClintonHillary Diane Rodham ClintonThe Memo: Trump furor stokes fears of unrest Bloomberg rolls out M ad buy to boost Biden in Florida Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close MORE should not pick a senator from a Republican-controlled state as her vice president, Senate Minority Leader Harry ReidHarry Mason ReidSupreme Court fight pushes Senate toward brink The Supreme Court vacancy — yet another congressional food fight Trump seeks to turn around campaign with Supreme Court fight MORE (D-Nev.) warned Monday. 

"If we have a Republican governor in any of those states, the answer is not only no, but hell no. I would do whatever I can, and I think most of my Democratic colleagues here would say the same thing," Reid told MSNBC's "AM Joy" when asked about the possibility of Democratic Sens. Elizabeth WarrenElizabeth WarrenOvernight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds On The Money: Half of states deplete funds for Trump's 0 unemployment expansion | EU appealing ruling in Apple tax case | House Democrats include more aid for airlines in coronavirus package Warren, Khanna request IG investigation into Pentagon's use of coronavirus funds MORE (Mass.) or Sherrod BrownSherrod Campbell BrownMnuchin says he and Pelosi have agreed to restart coronavirus stimulus talks Harris faces pivotal moment with Supreme Court battle Remote work poses state tax challenges MORE (Ohio) being named Clinton's No. 2. 
Reid added that he would "yell and scream to stop that." 
Democrats are fighting to regain control of the Senate majority this election cycle. They'll need a net gain of four seats to win back the chamber if they retain the White House, and a net gain of five seats to win the Senate back outright. 
While the 2016 map is tilted in favor of Senate Democrats — they are defending 10 Senate seats, compared to 24 for Republicans — a net gain of five seats is an uphill climb.
Both Warren and Brown, as well as Sen. Cory Booker (D-N.J.), are considered potential VP picks for Clinton and hail from states with Republican governors. If one of them were picked for vice president and Clinton won the White House, they would need to step down.
That could pave the way for a GOP governor to temporarily appoint a Republican to fill a Senate seat, forcing Democrats to win an extra seat to reclaim the majority. 
Brown, who has said he doesn't want to be vice president, has said that he's worried about allowing Republican Ohio Gov. John Kasich to fill his seat. 
"If I were on the ticket and Hillary were to win, that John Kasich would nominate and would appoint my successor, and that bothers me so," he told MSNBC's "Hardball" earlier this month.
But many have speculated that Brown or Warren would be stronger picks for Clinton, who may need to find a running mate that excites the liberal base after her bruising primary battle with Sen. Bernie SandersBernie SandersTrump, Biden will not shake hands at first debate due to COVID-19 Sanders tells Maher 'there will be a number of plans' to remove Trump if he loses Sirota reacts to report of harassment, doxing by Harris supporters MORE (I-Vt.).  
Warren and Brown are beloved by the left, party for their willingness to oppose trade deals and battle with Wall Street.
Updated at 1:21 p.m.