Lowe did hold preliminary discussions with Premier League chief executive Richard Scudamore following Glenn’s controversial move to White Hart Lane at the end of March.
The Saints chairman was investigating whether Spurs had broken any of the four clauses in the Premier League's code of conduct over the poaching of managers but has now decided against making a complaint.
Lowe said: "We considered all the options and in the end decided there was little mileage in it. There was no timescale imposed on it and we could have made a complaint at any time but we will not now be doing that."
Southampton chairman Rupert Lowe will not be making an official protest to the Premier League over the appointment of Glenn Hoddle as Spurs manager.