UH owns the wooded land bordered by Wheeler, MLK, Spur 5, and OST/Alt 90. I haven't seen any of their master plans indicate any planned use of it though some campus maps color it as part of the "medical district" of campus, which would work well with Khator's goal of starting our own medical school.
I've heard from people who would know, that it's university policy to not purchase any surrounding land. A theory is that Khator fears the university buying land will encourage developers to bring in gentrification at the expense of the historic Third Ward community.
Judging by how consistently packed The Nook and it's neighbors are, UH needs more campus-adjacent food and beverage options. There aren't really any good places for this though except the empty lot across from the rec, currently temporarily occupied by The Gateway on Cullen leasing office.
(UH is re-bidding of the campus food contract though after an internal audit recommended significant changes, such as making the Moody Towers dining hall into a 24-hour lounge with expanded power outlets and coffee options. The new contract would also include the choice of what to do with the old Chinese Star property, afaik. What effect this might have on The Nook et al.'s business is unclear.)
With the continued growth of off campus student housing complexes though, enough students may spread far enough off campus to support development on OST south of the park or on Scott St. between Elgin and I-45. I imagine it'd be 2-4 years though before it's clear whether such investment would be warranted by developers.