The long-serving duo joined the Baggies seven days apart from each other back in August 2007, and are currently enjoying their 11th seasons with the club.
They are now consulting an independent company about organising a special game to mark that achievement in the summer.
Albion will assist where possible, and it is likely to be staged at The Hawthorns, but the onus is on the players to set up the fixture and organise who will be involved.
It was initially suggested that a testimonial would take place at the end of this season, but it is now expected to form part of the next campaign’s pre-season schedule.
Brunt has played 359 times for Albion, putting him in the top 30 of the club’s all-time appearance list.
Morrison isn’t far behind after appearing 317 times for the club, although he’s been ravaged with injury this season.
Both players are contracted until the end of this campaign, although Brunt can trigger an extra 12 months with appearances.
In the past, testimonials were a way of generating money for the player in question, who would often be nearing retirement following 10 years at a club.
But now footballers earn astronomical wages, money raised is usually dedicated to charity.
The testimonial will be a part of Albion’s ‘Years of the Throstle’ celebrations, taking place throughout 2018.
It’s 140 years since the club was founded, 50 years since they last lifted the FA Cup, 40 years since the first appearance of the ‘Three Degrees’ in blue and white stripes and 25 years since the Second Division play-off final victory.
A reunion dinner dedicated to the victorious 1968 FA Cup winning side forms the ‘keystone’ of the celebrations, the club has revealed.