If the REIT is a publicly traded REIT, they generally would only take cash to invest in the REIT.
However, a private REIT may be able to accept a 1031 exchange. You’ll need to check if they would do it and at what amount. Some private REITs would accept property via a 1031 exchange, but they may have minimums and the investor will have to bear all the 1031 costs.
Your client should do their due diligence to make sure the private REIT is an appropriate investment for them.