Ex forest boss in line according to Rob Phillips
He most recently managed Qatar Stars League club Al-Duhail.
Cardiff are looking for their third manager of this season after sacking Mark Hudson earlier this month.
The Bluebirds are just three points above the Championship relegation zone in 21st position and are without a win in 11 games in all competitions following Saturday's 1-0 home defeat by Millwall.
France international Lamouchi, 51, was in charge of Forest for the 2019-20 campaign when they were pipped to the play-offs by Swansea City in a remarkable last-game turnaround on goal difference.
Ex-Ivory Coast boss Lamouchi, who most recently managed Qatari side Al-Duhail, had a distinguished playing career and won silverware with Auxerre, Monaco, Parma, Marseille and El Jaish in Qatar.
Like Lamouchi, Ismael has Championship experience with Barnsley and latterly at West Brom. He led Barnsley to the Championship play-offs in 2021 before heading to the Hawthorns, but departed Albion in February 2022 after a poor run of form.
Most recently Ismael, who led Austrian club LASK to their first Champions League play-off appearance, was coach at Turkish club Besiktas, where current Cardiff interim manager Dean Whitehead was part of his staff.
You do not have the required permissions to view the files attached to this post.