Labidi's father said Monday his son made suspicious phone calls over a 27-day period in December 2014 from unknown numbers on the island of Djerba, off the southeast coast of Tunisia.
"Yassine told the family he was with his girlfriend — an American of Iraqi origin and her family, and that he was calling from their foreign phones," he said.
Terrorist’s father stressed that there were no signs pointing to his son’s extremism.
“For example, he did not force his sister to wear a hijab, she does not wear one," he added.
On Friday, Tunisian Security Minister said that suspects behind Wednesday's deadly attack could have got their weapon training in Libya in December 2014.
More than 20 people were killed and over 40 persons were wounded during the attack. Most of the victims were foreign tourists visiting the museum.
The Islamic State militant group claimed responsibility for the attack on the museum.