The Sun reports that West Brom are hoping to land Berahino in a £12million deal this summer.
Berahino has a year left on his current contract at the Hawthorns.
Belgium striker Lukaku is expected to leave Everton this summer, with the likes of Paris Saint-Germain and Manchester United ready to make a move.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.