I'm not sure there would be a way to do this. The stocks would need to be sold in order to be converted to cash to buy the real estate, which would trigger capital gains regardless of if the stocks were held by you personally or transferred to an LLC.
This transaction also wouldn't qualify for a Section 1031 exchange because that requires that real property be exchanged for other real property and stocks are not included in the definition of real property.
The only potential option could be to transfer the stocks to a self-directed 401(k), but even then you may still have to sell the stocks prior to transferring them and may not be able to directly transfer the stocks in without triggering capital gains. You would want a retirement plan expert to comment on if this option could work.
Note: this post is intended to provide limited advice and should not, and cannot, be solely relied on. You should consult your own tax, legal and accounting advisors before engaging in any transaction.