Trainers on his knees?

I understand that ‘trainers’ can be the British equivalent to ‘sneakers’ but what does ‘trainers on his knees’ mean in the following passage?

Mrs Reynolds pointed at the little cream velvet sofa and he sat down carefully with his dirty trainers knees.

Does it mean he took his sneakers off and put them on his knees keeping them there while sitting on the sofa?

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Trainers in America are people who work in Sports medicine essentially. They take care of injured athletes. They can also be people who ‘train’ people in weight lifting and physical fitness in general.