Megson is in temporary charge of the Baggies following Tony Pulis's sacking earlier this week and, according to the Daily Mail, the 58-year-old took on the role under the condition that his younger colleague be excluded from training sessions.
The newspaper claims that Garner, 37, has "significantly" different methods to Megson, who is keen that the players are fully focused on his approach in the short-term.
Megson will be in charge for the Baggies' trip to Tottenham Hotspur on Saturday afternoon, with a managerial appointment expected shortly afterwards. Garner, who was linked with the Nottingham Forest job a year ago, will then be re-evaluated by the new boss.
Former Crystal Palace and Newcastle United manager Alan Pardew is the firm favourite to take over at The Hawthorns and could be in the dugout by the time West Brom welcome the Magpies on Tuesday night.