Several national papers have written that Strachan has been given permission to talk to Leeds.
However, Lowe sent an e-mail to Saints fans subscribed to the Saints club newsletter, stating: "There has been no formal approach from Leeds and no permission has been given.
"Any approach would have to come across my desk and it has not done so. And there is no suggestion that it will happen.
"I can only advise our fans not to listen to second-rate speculation and to check our web site for any updates.
"Gordon has been coaching the players as normal today (Monday) and had a very good session. They are all preparing as normal for what will be a very tough and very important game against Chelsea.
"Like me, he is a great believer that if you say anything then it can give a story legs so it is better to say nothing and not comment on speculation.
"We have better things to do than worry about rumour. If something happens then we will deal with it but it is business as usual.
"We are in a good position in the league and we have a lot to work for so fans should not let all this get to them."