Mourinho has replaced Paulo Fonseca at the Serie A side as Roma's ambitious new owner, billionaire US film director and producer Dan Friedkin, tries to fulfil his pledge to make them "one of the greatest names in world football".
Speaking to BBC Sport, Smalling is adamant there are no issues with the Portuguese.
"Ultimately, if the manager wasn't speaking about you and didn't want you to play and push, that is when you need to worry because he has stopped caring about you, he doesn't want you involved and he doesn't want you to play," said the centre-back.
"He is a born winner. He likes to push everyone to the limits. That is what he has done throughout his career and it has reaped results."