MEXICO CITY, Feb 12 (Reuters) - Mexican tycoon Carlos Slim is interested in increasing his investments in the oil sector, including in U.S.-based Talos Energy's projects, after the billionaire businessman bought a stake last year in a major offshore project discovered by Talos.

Speaking at a press conference, Mexico's richest person signaled he would like to grow his company's presence in the oil and gas industry beyond providing oilfield services, including possible petrochemical projects.

Slim said that increasing his stake in Talos' Mexican subsidiary would depend on other unspecified factors. He said he is especially interested in potential investments in Houston-based Talos' overall portfolio.

"It depends on the conditions," he said, referring to possibly growing the stake of his holding company Grupo Carso in Talos' local unit. "But definitely. Investing in the parent company ... interests us.

"We're interested in being partners with someone with experience," added Slim, whose business empire extends from telecommunications to mining to retail.

Talos discovered the Zama oil deposit in Mexico's territorial waters in the Gulf of Mexico in 2017, but later lost rights to operate the potentially lucrative find to state oil company Pemex, which holds the rights to an adjacent area where Zama likely extends. The Zama oil field, believed to hold around 735 million barrels of oil, is essentially Talos Mexico's only project.

Last September, Talos completed a $125 million transaction with Grupo Carso that involved the sale of 49.9% of its subsidiary Talos Mexico.

At the time, Talos CEO Tim Duncan stressed that 2024 would be "an important year for that asset," citing progress on engineering designs.

Over more than a decade, Slim's oil and gas business has mostly focused on providing services, like renting out drilling rigs and deep water platforms.

"We're involved in not just helping with drilling (services), rather we're getting involved in oil," he said, suggesting an ambition to possibly move into producing and marketing crude.

Slim said he currently holds about 22% of Talos overall.

Zama's operator and largest shareholder is Pemex, with a 50.4% stake, while Talos and Carso hold 17.4%. Germany's Wintershall Dea has another 19.8%, and Britain's Harbour Energy the remaining 12.4%.

Last week, Mexico's oil regulator approved a Pemex request to modify Zama's development plan. Pemex had sought to cut the budget from more than $1.24 billion to just under $70 million and delay some related infrastructure projects.

Zama is expected to eventually pump up to 190,000 barrels per day of medium crude and associated gas. (Reporting by Valentine Hilaire in Mexico City; Additional reporting by Marianna Parraga and Cassandra Garrison; Writing by David Alire Garcia; Editing by Brendan O'Boyle, Marguerita Choy and Leslie Adler)