Hutton spent the second half of last season on loan at the Stadium of Light, and Black Cats chairman Niall Quinn has confirmed his desire to sign the Scotland international on a permanent basis this summer.
However, Spurs chairman Daniel Levy is determined to secure at least the £9m he shelled out to sign Hutton from Rangers in January 2008, and a preliminary round of discussions has failed to persuade him to soften his stance.
Steve Bruce will not be spending £9m on a full-back, and the Sunderland boss has drawn up a list of alternatives in case an agreement cannot be reached.
Angeleri is understood to head that list, and with Bruce keen to have a signing in place when pre-season training begins in mid-July, the Black Cats are ready to call off their pursuit of Hutton and focus their attention on South America.
Angeleri spent last season with Argentinian side Estudiantes, and would be available for around £3m.
The 27-year-old was a surprise omission from Argentina's World Cup squad, with Diego Maradona expected to field a back four comprised entirely of centre-halves in South Africa.
Angeleri expressed a desire to change clubs after Estudiantes were knocked out of last season's Copa Libertadores at an early stage, and Sunderland officials are ready to lodge a formal offer for the full-back's services.
Provided that is accepted, they will immediately seek to fly Angeleri and his agent, Miguel Pires, over to England for talks.
The South American has been on the club's radar for a number of months, and Bruce's number two, Eric Black, travelled to Buenos Aires to watch Estudiantes at first hand earlier this year.
Bruce has enjoyed considerable success in the past signing players from South and Central America, and the trend could be set to continue when he renews acquaintances with scout John Benson later this summer.
The pair worked closely at Wigan Athletic to sign the likes of Wilson Palacios, Antonio Valencia and Maynor Figueroa, and Bruce was straight on the phone after Benson left the DW Stadium last week.
The 67-year-old will join Sunderland's scouting network in the next month or so, having spent 11 of the previous 15 years in a number of roles at Wigan including manager and director of football.
His close relationship with Bruce means he is likely to have a major input into recruitment this summer, and defender Michael Turner is hoping to welcome some high-quality additions to the squad prior to the start of next season.
The centre-half was one of Sunderland's flagship signings last summer, and having helped the club secure a 13th-placed finish in his first season on Wearside, he is confident of further progress in the next 12 months.
"The team has progressed from last year," said Turner. "You only have to look at the points tally and where we are in the league to see that.
"There were a lot of changes over the summer and I'm sure there will be some new additions to the squad during the close season. Hopefully, we can keep improving.
"I think we will be building from a greater position of strength this summer than we were 12 months ago, and that has got to help the manager in what he is trying to do."