Leicester have lost only one game in the league this season and are five points above second-placed Arsenal, who have a game-in-hand, in a tight table.
"We are not getting carried away at all. We will let the media speculate but we are going to stay grounded and take one game at a time, and see how far we can go," Morgan told British media.
"I thought we were playing well but didn't get the rub of the green at times last season. We made some mistakes that would cost us the game.
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"This season we have eradicated that and the results are coming."
Manager Claudio Ranieri insisted his team felt no pressure of being table toppers and called his team to stay calm and focus on the next match, having already exceeded expectations.
"Why should we play under pressure? Why stress? Last season they had stress, not this year. I think they're enjoying it and they must continue in this way," Ranieri told British media.
"If we make something special, it's a miracle. If it doesn't happen, what we're doing is already a miracle. They must enjoy playing."
Leicester next visit ninth-placed Liverpool on Saturday.
(Reporting by Nayan Das in Bengaluru; editing by Sudipto Ganguly)
