Both men were appointed at their respective Manchester clubs at the start of the 2016/17 season and were expected to battle it out at the top of the Premier League.
However, neither managed to get their team firing on all cylinders in their first season in charge, with United finishing sixth, while City were third.
Souness, a former Liverpool boss, believes their failures last season puts immense pressure on them to win Premier League silverware at the second time of asking.
He told Yahoo Sport: “We all thought it would be Guardiola v Mourinho doing battle at the top of the table last season, but City and United never even came close to getting into the title mix.
“Now they will be under pressure like never before because they are working for owners who expect to be challenging for the title.
“The record these two guys have confirms they are great managers, but they have probably taken on the biggest challenges of their career in these two jobs and they have to respond to the task.”