I have had the Target Red card since october 2015. Recently, seeing people getting upgraded to MC version, i decided to send a SM to the customer service couple weeks ago and here is the response i got from them:
Hi XXXX,
Thanks for taking the time to write us!
At this time, we're not opening new Target MasterCard accounts or accepting requests to upgrade existing REDcard accounts to the Target MasterCard.
We hope that you'll still enjoy the benefits of your current REDcard and use it in your local Target store and online at Target.com to save 5% and get free shipping every day. Click 'REDcard Benefits Program Rules' above for details.
Thanks for being a valued and loyal guest since 2015!
Sincerely,
Target Card Services, servicer to TD Bank USA, N.A.
This message was dated 6/17/2016
Going thru a divorce, i go to my previous house to pick up the kids for the weekend and my soon to be ex hands me an envelope from target, I open it and the date on the letter is 6/24/16 and the letter says they are happy to inform me that my target red card is being upgraded to target MC as of 8/25/16
One sign of this coming, which i did not get it at the time, is that i was bumped from $1300 to $4000 limit last month at the statement cut off. My last cli before that was a month before, in may, from $800 to $1300.
So if you guys get an unexpected high cli on your target card, it is a good sign that you will be upgraded to the MC version. If you call or message CS and they tell you it is not being done at the moment, like they told me, don't believe it. They are still converting them to MC, just don't know based on what.
Target has given me 2 bday gifts this year, a nice cli on my bday, from $1300 to $4K, then upgrading me to the MC version 
Congrats! That's good mail right there!!
Congrats and Happy Belated Birthday!! I hope to get a surprise like that on my birthday next month!