Clarke worked as number two to Mourinho and Avram Grant at Chelsea and had spells under Ruud Gullit and Sir Bobby Robson (Newcastle), Gianfranco Zola (West Ham) and Kenny Dalglish (Liverpool).
He received a text from Real Madrid supremo Mourinho ahead of Saturday's 4-2 win at Sunderland offering encouragement after Albion's flying start to the Barclays Premier League season.
But Clarke has been determined to do things his way since taking charge at the Hawthorns in the summer.
Clarke, whose third-placed side visit Swansea tomorrow evening, said: "Jose sent me a little text before the game at the weekend. It was a nice text.
"There were some good things in it although it's private between me and Jose.
"But it was about encouragement and just to keep going and to keep working.
"Did I give Mourinho any advice? The text was sent before his defeat at the weekend. I didn't. It's not for me to give Jose advice. He is (was) my boss.
"But I do just try and be myself on the training ground and in the press conferences.
"I always said when I took the job, although I've worked with a number of top coaches, I would just be myself.
"As you can tell, I'm quite a level-headed person and I try and convey that to the players as well."
Albion will be bidding to win a fifth successive top-flight game for the first time in 34 years at the Liberty Stadium.
But Clarke knows many testing hurdles lie ahead before he will allow himself the luxury of enjoying Albion's success.
He said: "This is where you get tested. This is a test of the squad, the character of the group.
"So far every time they've been tested, asked the question, they have passed the test, and there have been some pivotal moments.
"We have to keep facing those challenges and we have to keep our season on the right track.
"We are in a good place, are confident and want the games to come. We are not afraid of any games at any moment and we face the challenge head on.
"But we are not even into December yet. I'll get lifted by it all when we get to the last weeks of the season.
"If we are still in a good position then, then I'll enjoy the moment.
"At the moment I just have to keep working game to game. I know it is boring for you guys and you want me to get carried away and say 'we are going to do this, that or the other.' We are not."
Clarke will take a careful approach to the calf injury suffered by key defender Jonas Olsson during the win at Sunderland.
He said: "My job is to manage the squad. Jonas has played every game, one of the few who has played in every game for us.
"He is a tough character. He will play through the pain barrier if he has to and I've got to manage it and make the right calls.
"I've got to make sure I've got players for the long term and not just for the next game."
Goalkeeper Ben Foster is again ruled out with the groin problem which could require further surgery and Boaz Myhill will deputise for the fourth successive match.