The Shard builder played a key role in the delivery of the London Olympics projects.
"It has been worrying in the last 3 months as there has been a reining back of a commitment to fund projects," Pycroft said.
"Every client we speak to is constrained by a lack of bank finance.”
Qatar was controversially awarded the World Cup for 2022 last year, and a project management role for the construction of the stadia is likely to be awarded imminently.
“Qatar are looking for the best people in the world ... We're one of five, everyone's been interviewed, and the view is that they will decide on somebody before December," said Pycroft.
Mace currently operates in 67 countries, and is looking at emerging markets such as the Middle East and the East Coast of Africa as the European market remains stagnant.