July 13 (Reuters) - I Squared Capital will invest up to $2 billion in the Saudi Arabian sovereign wealth fund's real estate and infrastructure assets in the country, both parties said in a joint statement on Monday.

The asset manager will invest up to $1 billion each in undisclosed digital infrastructure and district cooling assets of Saudi Arabia's Public Investment Fund, with the option to scale across other related business themes.

District cooling plants deliver chilled water via insulated pipes to cool offices, industrial and residential buildings.

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

PIF's unit, King Abdullah Financial District, was seeking to sell its district cooling assets for more than $500 million, Reuters reported in March, citing two sources.

The capital injection into Saudi Arabia comes as Riyadh seeks funds to diversify away from its vast oil-dominant economy, illustrated by PIF's investments in European sports, video games and SpaceX, among others.

I Squared, meanwhile, is no stranger to digital assets, having acquired 10 data center facilities in the U.S. from Cogent Fiber in May.