MLB has sued Biogenesis of America and its operators, accusing them of scheming to provide banned PEDs to players in violation of their contracts.
(Read More: How a Hockey 'Bad Boy' Helps Athletes Invest)
Miami New Times reported in January that it obtained purported records detailing drug purchases by Rodriguez, Cabrera, Cruz and former AL Cy Young Award winner Bartolo Colon.
Yahoo Sports reported that Braun, the 2011 NL MVP, was mentioned in the records.
Most have denied the Biogenesis link, although Rodriguez has admitted using performance-enhancing drugs earlier in his career and Colon and Cabrera each were suspended for 50 games last year for testing positive for elevated testosterone levels.
Braun failed a drug test in 2011, but his suspension was overturned by an arbitrator. He has acknowledged that he was mentioned in Biogenesis records because his lawyers had used Bosch as consultant during the appeal.
After the Brewers' 4-3 win in 10 innings over Oakland at Miller Park, Braun said he was done talking about the clinic.
"I've already addressed everything related to the Miami situation. I addressed it in spring training. I will not make any further statements about it," he said.
"The truth has not changed," he said.
Braun said the speculation was not affecting him on the field.
"No, of course not. I've dealt with this for two years now. I'm pretty good at avoiding distractions," he said.