The 22-year-old is out of contract in the summer but the Baggies may face competition from elsewhere, with both Everton and Real Sociedad - currently managed by former Everton and Manchester United boss David Moyes - reportedly interested in signing the player on a free transfer ahead of next season.
In terms of West Brom signing him, Ameobi is the kind of player that seems to fit into the style that Pulis likes in his teams.
Signing Ameobi would certainly give some extra pace to the side going forward, and could offer a threatening delivery from out wide to cause their opponents problems. Maintaining their Premier League status would of course be paramount to their chances of securing his signature.
Everton's recent run of results means their relegation fears from a few weeks ago have been eased considerably and wide areas could be an area for them to address with Kevin Mirallas being linked with a move away by the Mirror earlier on this season. The opportunity for Ameobi to go abroad to continue his development, but under a British manager, could be tempting to anyone in his position.
West Brom are currently seven points above the relegation zone and one would think they will find enough between now and the end of the season to ensure they will be playing in the top flight next season, thus enhancing their chances of landing the player.