Former Argentina coach Loffreda has left Welford Road just six months into what was thought to be a two-and-a-half-year contract after taking the Tigers to two finals - the Guinness Premiership and EDF Energy Cup - but losing both.
That failure cost him his job and the Leicester board are now considering their options.
They must now decide whether to pursue another overseas appointment, or keep their coaching structure in-house.
White has not been involved in coaching since his Springboks contract expired after South Africa's 15-6 World Cup final victory over England in Paris last year.
He has been linked with several subsequent jobs, including head coach of England and Ireland, and Leicester - five times Premiership champions and twice Heineken Cup winners during rugby's professional era - could prove an attractive proposition.
An internal reshuffle is possible, given that former England internationals Richard Cockerill and Neil Back were part of Loffreda's support staff, while another Leicester and England favourite Austin Healey has repeatedly been linked with a backs coaching job.
Loffreda though, who masterminded Argentina's third place in last autumn's World Cup - the Pumas beat France twice and Ireland - has paid the price for falling short of Tigers' immense standards.
Announcing Loffreda's exit, Leicester chairman Peter Tom said: "The board of Leicester Tigers has come to this decision after conducting its review of the playing season and in assessing what we believe is required to achieve the club's aspirations for the future.
"Marcelo arrived at Leicester Tigers in 2007 after leading Argentina to third place in the Rugby World Cup, and our decision has been taken with a degree of sadness.
"But we have taken this course of action in the best interests of the club, and we felt that this had to be done now to allow everyone to prepare fully to meet the challenges of the new season.
"On behalf of the club, the board would like to wish Marcelo and his family well for the future.
"No decision has been made on a new appointment, but we expect to have a new rugby structure in place ready for the players' return to pre-season training."