According to Darren Wolfson on Twitter, the Twins have not been in contact with Wheeler's agent for the past two and a half weeks:

The #Twins haven't maintained dialogue w/ free agent Dan Wheeler's agent for 2 1/2 weeks now. In other words, seems like that door is shut.
In the past three seasons, Wheeler has held right-handed opponents to a .195 average with a very good 5.8 strikeouts-to-walks ratio.