Shaw picked up an ankle injury against Southampton two weeks ago, whilst Bailly was hospitalised due to a head injury caused by a freak collision with Harry Maguire in the FA Cup semi-final against Chelsea.
‘Axel and Phil are out but the others, I’ll give enough time to prove their fitness,’ Solskjaer said.
‘We’re looking forward to the game, we’ve given ourselves a good chance of being in the Champions League next year but we can’t go into the game thinking what the outcome could be.
‘We’ve just got to perform at a high enough level and standard so we can get a result.’
If fit, Shaw will almost certainly be recalled to the side as they have struggled defensively since his injury.
However, despite dropping points at home to Southampton and West Ham and crashing out of the cup to Chelsea, United’s form is better than that of Leicester.
The Foxes have only picked up nine points in eight Premier League games since the restart and have seen their 16 goal advantage in goal difference over the Red Devils whittled away to zero.
To make matters worse, they are without James Maddison, Christian Fuchs, Ben Chilwell, Caglar Soyuncu, Daniel Amartey and Ricardo Pereira and possibly Marc Albrighton, who faces a late fitness test.
Martin Atkinson, who also presided over the reverse fixture at Old Trafford, will be the referee, with Paul Tierney on VAR duty.
United need a point from the game to finish in the top four and qualify for next season’s Champions League. A win would ensure the Reds finish in third place regardless of Chelsea’s result against Wolves.
If United were to lose to Leicester, they would then only qualify if Wolves beat Chelsea at Stamford Bridge.
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