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The Man United boss also aimed a subtle dig at Premier League rivals Manchester City and Chelsea.
In the build up to Liverpool's clash against Burnley, Klopp questioned Man United's big-money deals, saying: "What United are doing, I don't know how they did it."
Solskjaer has since responded to Klopp and jokingly admitted that he's now driving an electric car in a shot at oil-rich clubs Man City and Chelsea.
Speaking ahead of his side's fixture at Southampton, he said: "We are a well run club.
"We do have a lot of fans out there and we do have good sponsorship deals.
"How we get the money, as a manager you want more and more. I have heard 'no' a few times.
"How other clubs run their clubs, there are different models at different clubs.
"I have started buying electric cars! That is all I want to say about that situation."
Solskjaer has splashed the cash on Jadon Sancho and Raphael Varane, with both players available for their St Mary's clash.
Man United will be looking to make it two wins from two games following their drubbing of Leeds last weekend.
Bruno Fernandes starred as he bagged a hat-trick in their 5-1 win at Old Trafford.
Featured Image Credit: PA/Football Daily
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