In a message sent to Mukherjee's office, Dr Momen described him as a great friend of Bangladesh.
The Foreign Minister said he had the opportunity to meet Mukherjee when he was a Minister during 1973-1974.
"My first visit was to India after I had taken over responsibility as Foreign Minister," Dr Momen said.
He said he visited Mukherjee's official residence with his wife and invited him to join Bangabandhu's birth centenary celebrations.
"I expect he will soon visit Bangladesh after recovering quickly" said the Foreign Minister.
Read Also: Ex- Indian president Pranab Mukherjee on ventilator after surgery
Meanwhile, State Minister for Foreign Affairs M Shahriar Alam also prayed for speedy recovery of former President of India and one of the greatest friends of Bangladesh who went through a brain surgery and tested positive for COVID-19.
Earlier, Pranab Mukherjee confirmed that he tested positive for COVID-19.
"On a visit to the hospital for a separate procedure, I have tested positive for COVID19 today. I request the people who came in contact with me in the last week, to please self isolate and get tested for COVID-19," he tweeted.