It will be worn for the first time on Saturday, when they face Perth Glory in a pre-season friendly in Western Australia.
United finished sixth in the Premier League this past season, with Solskjaer coming into the fold to replace Jose Mourinho midway through the campaign before signing a permanent contract to stay on as manager.
The Nerazzurri have not presented a new offer yet as they only held formal talks with United on Thursday.
"I think we are starting to understand it all a bit better".
The 26-year-old's mood was unlikely to have been lifted when Rashford was handed a bumper new £300,000-a-week deal last month, further highlighting the fact Lukaku has fallen behind the academy graduate in the pecking order.
He told talkSPORT: "I just think he's walked into a mess and he's got such a hard job".
Marco Asensio and Casemiro are two players that I failed to mention before, but there are more than enough quality players within the squad now with only three spots to fill.
"He knows if he keeps on with these players and doesn't change the personnel, he'll get sacked".
Scroll through the mini-gallery to see some images of United's new away kit!
Solskjaer on Wednesday accused the media of having an "agenda" when it comes to Pogba, who he called "a top bloke" and "a great professional".
It really does seem that nothing will happen down the Red Devils' end unless Paul Pogba is sold, and, as things stand, that seems somewhat unlikely.
Inter sporting director Piero Ausilio was in London yesterday to meet United officials but was left in no doubt that their current proposal would not be good enough as they struggle to meet the Premier League club's valuation.