The former PSV striker had several bust-ups with United coach Alex Ferguson after the Dutch player was relegated to the bench for the majority of last season's campaign.
Their row peaked when Van Nistelrooy pulled out of the team's final game of the season against Charlton after knowing he wasn't in the starting line-up.
"Ruud hopes to announce a new club before he has to be in training with Manchester on July 24th," Linse told De Telegraaf.
Following a mediocre participation with Holland at the World Cup in Germany last month, Van Nistelrooy was linked with Real Madrid and Bayern Munich.
While Spanish media had reported that the 30-year-old star already agreed to join Real Madrid, Linse insisted the deal is contingent on United's decision.
"Only if Manchester United reaches an agreement with a club, will I respond to reports," he said.