The influential centre-back has missed City's last 10 games after suffering a thigh injury two months ago.
The Belgian has been back in full training for the past week and will be considered for the trip to The Hawthorns.
Manager Manuel Pellegrini said: "Kompany is in the squad list and he is travelling with the team."
Kompany has been sorely missed throughout his absence, with the defence looking vulnerable and the team suffering damaging defeats at Chelsea and Sunderland.
Some of those deficiencies have been masked by City's attacking brilliance during that spell and Pellegrini has downplayed them, but the skipper will be welcomed back.
Pellegrini said: "I think Vincent is a very important player. He is a very good defender and of course we need him.
"On the other side, in the last five (domestic) games just Sunderland have scored one goal (against us). In all the others we have had clean sheets.
"So the other defenders can do it as well, but Vincent is always an important player."
Kompany's possible return is timely with fellow centre-back Matija Nastasic currently ruled out with a calf problem.
The other players still sidelined are playmaker David Silva and striker Stevan Jovetic.
The West Brom clash will be the first test of City's indifferent away form since the Sunderland loss on November 10.
In contrast to their 100 per cent home record - which features 7-0 and 6-0 thrashings of Norwich and Tottenham respectively in the past month - City's away performances have threatened to undermine their title challenge.
Pellegrini's men have lost four of their six league games on the road but the Chilean continues to insist the approach for all games will remain the same.
He said: "It is very important especially this week.
"We play two games away before we play against Arsenal here at home so I hope we will be the same team we are here in those two games this week."
City have declined to comment on a report they have struck a deal potentially worth up to £2.4million for 14-year-old Malaga player Brahim Abdelkader Diaz.