July 13 (Reuters) - A joint statement issued by I Squared Capital and Saudi Arabia's Public Investment Fund on Monday showed that I Squared Capital will invest up to $2 billion in the fund's infrastructure and real estate assets.

Isquared Capital Asset Management will invest up to $1 billion in digital infrastructure assets and another $1 billion in district cooling assets, both belonging to Saudi Arabia's Public Investment Fund, with the potential to expand into other related business areas later. The two parties did not disclose details of these assets.

Central cooling systems rely on distributing chilled water through a network of insulated pipes to cool offices, industrial and residential buildings.

This deal comes more than a year after the two parties agreed to develop a dedicated infrastructure investment strategy focused on the Middle East region.

Reuters quoted two sources in March as saying that the King Abdullah Financial Center, which is part of the Public Investment Fund, was seeking to sell its district cooling assets for more than $500 million.

The injection of capital into Saudi Arabia comes at a time when Riyadh is seeking to attract more funding to diversify its economy away from oil, which largely dominates its economy, as evidenced by the fund's investments in European sports, video games, SpaceX, and other investments.

Isquared Capital has a strong presence in the digital infrastructure sector, having acquired 10 US data center facilities from Cogent Fiber in May.