Wayne Rooney Snr is one of nine men who were arrested on Thursday in a probe into betting irregularities.
But Capello said the striker was "relaxed and calm" about the situation ahead of the Euro 2012 qualifier.
"He told me 'absolutely no problems'," the England manager said. "He is sure this poses no problems."
England captain John Terry added: "Wayne is focused on the game. We all realise the importance of that. It is important for him to go and play his football. That's all that matters to us."
Capello said it would be a "big mistake" if England played for a point - all that is needed to secure qualification - in Podgorica.
Continue reading the main story 3 September 2010 - England 4-0 Bulgaria17 September 2010 - Switzerland 1 England 312 October - England 0-0 Montenegro26 March 2011 - Wales 0-2 England4 June 2011 - England 2-2 Switzerland2 September 2011 - Bulgaria 0-3 England6 September 2011 - England 1-0 Wales"We need to play to win," he said. "I think the players understand we need to play the same level we play always away from England.
"I hope our play tomorrow will be really good for us to qualify in first position."
Capello said he had not yet decided who to partner with Rooney in attack for the match.
Asked whether fellow Manchester United striker Danny Welbeck may get the call, Capello said: "I need to sleep on this tonight. We will decide tomorrow morning about the forward we will play with Rooney and also the right-back."
Tottenham's Kyle Walker and Manchester United's Phil Jones could be in line for that defensive role.
"One of those players will play tomorrow and I have confidence in them," Capello said.
Meanwhle Terry, who was captain in England's unsuccessful Euro 2008 qualifying campaign and part of the side which underperformed at last summer's World Cup, sees Euro 2012 as an opportunity to make amends.
"It's obviously my dream to take an England side into a big, major tournament," he said.
"With that in mind as a personal goal that's my target.
"Collectively for the team [qualification] is the priority, whether with a draw or a win.
"We're full of confidence, playing well, hence why we're top of the group. We must get ourselves over the line tomorrow."
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