I'm not convinced Sturridge was his choice at all. Weren't the club trying to get Sturridge whilst Kenny was in charge? I've no idea about Coutinho but if you read this article from around when he signed he had aleady been monitored by the club before Rodgers was even at the club
www.bbc.co.uk/sport/0/football/21236041
The relevant bit being
New manager Claudio Ranieri sent Coutinho on loan to struggling Spanish side Espanyol for the second half of the following season. He impressed, scoring five goals in 16 appearances.
This was when Liverpool first showed an interest in the player. Benitez had told their
director of football, Damian Comolli, that Coutinho was the best young player at Inter and capable of being a big success in the Premier League.
Inter had yet another new manager, Andrea Stramaccioni, by this time, though, their sixth during Coutinho's time at the club, and he wanted to keep the player, so Inter rebuffed Liverpool's offer.