Hull goalkeeper McGregor missed this week's friendly encounters with the United States and Norway because of a thigh injury.
In his absence, Cardiff's Marshall has recorded two clean-sheets and was magnificent as the Dark Blues survived a barrage in Molde before completing a 1-0 smash-and-grab victory over the Norwegians on Tuesday.
Scotland boss Strachan said: "I've known David for a long time and he's now got a presence about him that he didn't always have.
"It's not arrogance, it's just a self-confidence. He hasn't changed off the pitch. He's still a very quiet and unassuming man but there is now a presence on the pitch.
"Is he now putting Allan McGregor under pressure for the number one spot? Yeah, I think he is."
Strachan replaced Craig Levein as manager in February after his predecessor's side failed to win any of their first four World Cup qualifiers.
The former Celtic boss could do little better in his first two competitive matches as they lost to Wales and Serbia.
But an away win over Croatia in June raised spirits and the nation are currently riding high after extending their unbeaten run to four matches with Scott Brown's winner on Tuesday.
Strachan admitted his side were poor at the Aker Stadion in Molde but believes his side are making strides forward.
He said: "We won, but Norway were the better side. I don't want to have to go through that again. That's not what I'm aiming for.
"We take comfort from one or two things but we want to better than that and we can be.
"Has the first year gone as well as I'd have hoped? Well I'm still in a job. That's what you try and achieve in your first year in management.
"I'm enjoying working with the lads and the longer it has gone on the more pleased I've been, especially after a poor start.
"That start affects people and tests your mentality. But it's good to be here picking up another victory. That keeps us going for another three and a bit months until the next game.
"I look back to the Wales game and that was a long night. I'm getting better sleeps now."