United's pre-season tour of Australia has been overshadowed speculation over the futures of several stars, including De Gea who is in the last year of his contract and has been linked with French champions Paris Saint-German.
The Spaniard is reportedly near marking another five-year manage United worth in excess of £350,000 every week that would make him the most generously compensated goalkeeper in the world.
De Gea was refreshed from United's pre-season opener against Perth Glory on Saturday however will arrange against Leeds on Wednesday to wrap up the Red Devils' 10-day visit toward the Western Australia city.
'He'll play and hopefully, we can agree (on a new deal) with David, as I've said a few times,' Solskjaer told reporters.
'That'll be up to David to announce when that happens, if and when.'
The United manager wouldn't be drawn on whether Leicester City and England center-back Harry Maguire was headed to Old Trafford.
'There's been loads of speculation but I can't really say anything,' Solskjaer said.
'There's a limit of players and whoever performs will be part of the team and whoever doesn't they will have to fight to get back in.'
After an unconvincing 2-0 triumph over an exhausted Perth, United will seek after a superior execution against one-time severe for Leeds.
The competition has stewed since Leeds' assignment from the English Premier League in 2004 yet threats between the enthusiastic fan bases are as yet obvious with additional safety efforts being set up by coordinators at Perth Stadium.
Solskjaer said United were excited to renew the rivalry. 'Of course, you want to have games against the biggest clubs,' he said. 'It's a great occasion for both sets of supporters and the players because there were great games (in the past).'
Romelu Lukaku, who is reportedly hoping to tie down a transition to Inter Milan, is set to play his first pre-season match against Leeds after recuperating from a 'niggle'. Nonetheless, Luke Shaw is probably going to pass up a major opportunity subsequent to enduring hamstring damage in the match against Perth.
United will have further pre-season games against Inter Milan in Singapore on July 20 and Tottenham in Shanghai on July 25, while Leeds will head to Sydney to face Western Sydney Wanderers.
