Chelsea claimed a Premier League-record 30 victories under the stewardship of Conte, including 13 in a row from October 1, to finish seven points ahead of second-placed Tottenham.
"It's flattering that a club like Barcelona can be interested in you", he said.
Despite Chelsea's success over the last 15 seasons, a Blue manager had not yet received the award from the LMA.
Meanwhile, Brighton manager Chris Hughton bagged the Championship award for leading the Seagulls back to the top flight for the first time in 34 years. "It's a great achievement for me and I hope to continue in the best way and deserve this award".
The Italian is only the third foreign victor of the prestigious award after Claudio Ranieri picked up last year's prize and Arsene Wenger, who won the accolade in 2002 and 2004.
The Italian was awarded manager of the year and Premier League manager of the year for bringing the title back to Stamford Bridge. Brighton finished second to Newcastle in this year's Championship. It's all about hard work, I've never worked so hard in my career and I just want to keep on improving in the position I'm playing.