The Swans are in top-flight of English football for the first time in 28 years after qualifying through the Championship play-offs last season.
And manager Brendan Rodgers is keen to strengthen the squad ahead of the new campaign.
According to The Daily Mirror, the Welsh club are hoping to snap up the services of Trezeguet, who is a free-agent after leaving Spanish club Hercules.
The 33-year-old was part of France's triumphant 1998 World Cup team and scored 34 goals in 71 internationals for Les Bleus.
Meanwhile, Swansea have agreed a £1.5million fee with FC Utrecht for Dutch goalkeeper Michel Vorm.