Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
Loan pair Sam Hutchinson and Leon Best have extended their deals at Sheffield Wednesday.
The 20-year-old Brazilian became manager Brendan Rodgers' second signing of the January transfer window after finalising the details of his medical and work permit in an £8.5million switch from Inter Milan.
Midfielder Lucas revealed he advised both Rodgers and the player ahead of a deal which the Brazilian believes can prove an all-round winner.
"The manager spoke with me, not asking me about his talent, because he was sure about his talent, it was just about how he was as a person," said Lucas.
"I spoke to him (Coutinho) a few times, not trying to convince him to sign, just telling him about the club, how things work here. He just felt it was a great opportunity for him to come to the Premier League and we are happy to have him here.
"Coutinho is a very talented player, with a lot of experience for someone so young.
"He is a proper Brazilian with a lot of skill, he likes to play with the ball.
"He had a very good spell with Espanyol and I think he will be a great player in the future for us."
Coutinho is on his fourth club - all in different countries - in three years, but Lucas is confident he will quickly adapt to life in the English top flight and his transition to Merseyside helped by the Reds' South American contingent.
"In Italy, it is a different game, but he has experience in La Liga as well. But I think he will be able to cope, I just hope he settles very quickly," said Lucas.
"We have Luis (Suarez) and (Sebastian) Coates, and myself, so we will all try to make him feel really comfortable and help.
"He is a young lad so we just need to make sure he settles very quickly, like Luis and Coates have, then he will be able to feel comfortable, show his qualities and start to play really well."
Doni joined the Reds from Roma in 2011 but made just four first-team appearances, his last involvement coming on the last day of last season at Swansea.
The 33-year-old Brazilian did not feature in the current campaign and slipped further out of the picture when Brad Jones was favoured as a replacement for the injured Jose Reina.
Liverpool, meanwhile, will be aiming to build some momentum with a positive result at Manchester City on Sunday after their midweek draw at Arsenal.
Reds boss Brendan Rodgers recalled his first-team regulars, having been criticised for his team selection in the FA Cup fourth-round defeat at Oldham.
For an hour, everything was going to plan as Jordan Henderson added to Luis Suarez's early goal to give the visitors a commanding 2-0 lead.
However, the Gunners suddenly kicked into life to make up for their defensive shortcomings as two quick goals saw them level through Olivier Giroud and a blistering strike by England forward Theo Walcott.
Brazilian Lucas feels even if they could not see the game through, Liverpool can now head into Sunday's showdown with City at the Etihad Stadium all set to produce another determined display.
"We were responding very well from the FA Cup tie. We showed a lot of attitude and the right mentality at Arsenal, we just have to keep going to get the points against Manchester City," the defender said.
"We didn't win at Arsenal, but we showed we are capable of fighting against and beating the top teams.
"This weekend we will have another opportunity to get a good result against a top team."