Both players are represented by Gregory Dakad, the same agent who looks after new Gers defender Bilel Mohsni.
Mali international forward Sidibe left Stoke last season after eight seasons with the Potters, during which time he was also on loan at Sheffield Wednesday and Tranmere.
The 33-year-old had previously played in the English lower leagues with Swansea City and Gillingham.
Bouazza, meanwhile, is available as a free agent having most recently played in Spain with Racing Santander, where he was a team-mate of ex-Rangers defender Carlos Bocanegra last season.
The Algerian winger, 28, also has extensive English experience having represented seven clubs there including Fulham, Charlton, Watford and Blackpool.
No talks have taken place as yet and McCoist is simply keen to assess the pair before he considers whether to take things any further.
He said: "The boys are two players who Gregory looks after and they'll be well known to people who know their English and European football. They've just come in to have a look at our place and also for us to have a wee look at them. This is their first day as they came into the city last night.
"They trained this morning and they were absolutely fine. They're obviously not up to the same levels of fitness as our lads are but that's totally understandable. They haven't done any pre-season training yet and there's no pressure on anybody. We'll make them feel very welcome and we'll see what happens.
"It would be crazy of us not to take the option to bring other people in and have a look at them after the success we've had with Bilel's trial. Both players have good pedigree."
Rangers will travel to Dundee on Wednesday night for a friendly at Dens Park and the manager refused to rule out involving them. He added: "I've not even thought about that yet and I've not asked either of them if they want to play. That's maybe something we'll look at in the next 24 hours."
- Sports & Recreation
- Mamady Sidibe
- Hameur Bouazza