"We've had the best year for 28 years and we've got a semi-final this summer and a European Championship that's predominantly at Wembley, providing we take care of business to qualify.
"So it's a hugely exciting time with the team. I don't think we've progressed as far as we can yet. I think there's room for us to grow."
The 48-year-old added: "I am still a young coach. I've managed less than 200 matches, so, for me, it's an honour to be in the role I'm in and I thoroughly enjoy it."
Southgate has been tipped for the United job (Image: GETTY )
Southgate has been a success as England manager (Image: GETTY )
Solskjaer has won seven games out of seven since - beating Sir Matt Busby’s record of five wins - to kick off his United management career.
And the Norwegian has become a genuine contender for the permanent role.
United are expected to speak to Tottenham about Mauricio Pochettino but Solskjaer appears to be the second favourite after impressing in the hot seat.
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Man United: Solskjaer should get job PERMANENTLY says pundit