The North-East club sit 16th in the Championship after 12 games and are now under the temporary charge of Mowbray's assistant Mark Venus, who has remained at the club.
Venus could well be given the permanent position but a club of Boro's stature are likely to appoint a name with more management experience.
Here, Sports Mole casts its eye over five early names being linked with the role.
Pulis's seven-year stint in charge of Stoke City ended earlier this year after the 55-year-old had guided the Potters into the top flight and made them into an established Premier League club. His style of play is known for its directness and lack of creativity but he could be just the sort of person to steer Boro away from the drop zone in the Championship. The clear early favourite with the bookmakers.
Clough lost his job at Derby County at the end of last month in what was viewed by many as an unfair sacking. The 47-year-old is said to be keen to get back into management quickly and has been heavily linked with the vacant position at League One club Sheffield United. If Clough doesn't take charge of the Blades, then he is likely to be interested if approached for the Boro job.
Considered a shoo-in by many for the Republic of Ireland job when Giovanni Trapattoni left the post, O'Neill has now been overtaken by Mick McCarthy as favourite to replace the Italian. If McCarthy is selected by the FAI for a second time then O'Neill could well be tempted by the Boro job, although his Premier League pedigree suggests that he could aim for a top-flight club if another boss is sacked in the not-too-distant future.
Current Hartlepool manager Cooper may not have as much managerial experience as the names around him here but his 15-year spell as a Boro player over two stints would make him a popular choice with some. The 46-year-old also had a brief time as caretaker boss of Boro in 2009 and was unbeaten in two games, winning one and drawing the other.
TV pundit Souness would certainly be viewed as a wildcard appointment as he has been out of the management game since early 2006 when he was sacked as Newcastle manager. Again, the 60-year-old's 200-odd appearances for Boro in the '70s would make him a popular choice but it would take a lot to tempt him back into management.