The 24-year-old has been linked with a move to the Manchester City.
The first leg will take place on August 16 at the Emirates Stadium.
The Chilean star will leave Udinese after five years with the club.
The 22-year-old is one of the most sought-after players of the summer transfer window.
Barcelona and Manchester City are vying for the 22-year-old winger.
Negotiations between Udinese and Barcelona hit a stumbling block late on Tuesday.
Sanchez was signed by Udinese in 2006 for USD 2.8 million.
Manchester United manager Alex Ferguson had wanted to sign the player last season too but the deal fell through midway.
Barcelona are ahead of Manchester United, Juventus and Manchester City in the race.
Udinese held AC Milan to a 0-0 draw that concluded the Serie A season.
Udinese is one of four clubs still jockeying for key positions in the final Serie A round.
Udinese enters fourth with 65 points, followed by Lazio with 63, Roma with 60 and Juventus with 57.
Also, Lecce won 2-0 at already-relegated Bari while AS Roma suffered 2-1 loss against Catania.
Gokhan Inler and German Denis scored the goals.
Udinese moved within one point of a Champions League spot with a 7-0 rout of nine-man Palermo.
Udinese beat Inter Milan 3-1 and Bologna also win by the same margin against Lazio.
Giandomenico Mesto scores as Genoa get the better of Udinese by a solitary goal.
Antonio Di Natale was Serie A's top scorer last season.
Juventus to beat Udinese to move within five points of leaders Inter Milan.
Wesley Sneijder netted his first Inter Milan goal in stoppage time.