No - There is no time limit specified in the laws of the game in regards to how quickly a player must leave the field when being substituted.
Law 3 The Players
3. Substitution procedure
the player being substituted:
must leave by the nearest point on the boundary line
unless the referee indicates that the player may leave directly and
immediately at the halfway line or another point (Page 50)
Also note that the time a substitution takes should be added as Extra Time.
Law 7 The Duration of the Match
3. Allowance for time lost
Allowance is made by the referee in each half for all time lost in that half through:
• substitutions (Page 83)
Also note that the referee has the power to caution a player that delays the game when being substituted.
Law 12 Fouls and Misconduct
3. Disciplinary action
A player is cautioned if guilty of:
• delaying the restart of play (Page 108)
Delaying the restart of play
Referees must caution players who delay the restart of play by:
• delaying leaving the field of play when being substituted (Page 110)
IFAB (FIFA) - Laws of the Game 2019/20