While England's relationship with Tottenham manager Harry Redknapp has virtually broken down, the respective medical teams have liaised harmoniously over King this week, as have Spurs chairman Daniel Levy and Capello's right-hand man Franco Baldini.
It was first suggested last year that King might see a Juventus doctor who has had some success in treating injuries similar to the 28-year-old's chronic knee problem.
Tottenham felt that King, who travelled last year to South Africa and the United States to meet various experts, had seen the top specialists and did not initially take up the offer. However, sources have confirmed that the Spurs medical team remained open-minded about receiving any fresh help that could ease the problem.
There is, though, an acceptance on all sides that Tottenham's approach this season has been generally successful, with King playing in 22 matches, double what he managed over the whole of the 2007-08 campaign.
With King having withdrawn from the England squad on Tuesday, Capello oversaw a training session yesterday that was sat out by Peter Crouch, who has a calf injury, and Shaun Wright-Phillips, who is troubled by an ankle complaint.
With 8,000 tickets remaining for the friendly match against Slovakia on Saturday and 10,000 still unsold for the qualifier against the Ukraine on Wednesday, Wembley should be close to capacity for both fixtures.
The best performances under Capello have come away from home but there is a hope that the next two games can see England build on the 5-1 Wembley win against Kazakhstan last October that came to be overshadowed by the booing of Ashley Cole.
"We want to put in a really good performance to get the crowd behind us," Emile Heskey said. "Once we have the fans behind us they're like a 12th man."
Matthew Upson, who in the absence of King is expected to be the main cover at centre-back for Rio Ferdinand and John Terry, added: "It's important and I think it's something we really need to work
on to bring that level of performance from our away games back to Wembley. A lot of people have said that perhaps we haven't performed as well as we should at the new Wembley, and they've probably got a right to say that.
"I think it's up to us to understand why we haven't performed and put that right and get some really good team performances and good results there. It's such a fantastic arena to play."