The boss takes charge of the Anfield club for the first time in the Premier League this weekend, with his most recent signing settling into his new surroundings after completing a £15 million move from Swansea City.
And when discussing how Allen has adapted to life on Merseyside, Rodgers told the club's official website: "Yes [he could feature against West Brom].
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"We got the go ahead [to sign him] at the weekend and then he went away with his international team.
"I'm sure he's enjoyed his first couple of days here. Like I said to him, I was afforded a great welcome here by the people, the players have been brilliant since I've been here - and I'm sure it's been likewise for him, but you'll need to ask him that."
Focusing on the squad and the Premier League kick-off as a whole, Rodgers revealed that he has made the majority of his team selection decisions already, but is wary of the few who have been away on international duty this past few days.
"I normally have a good idea in relation to what the team will be, but there are obviously considerations I'll need to make in the next couple of days in terms of players coming back and their fitness," he continued.
"In terms of tactics and my thoughts on the game, I've already got my team in mind.
"We had 16 players training on Wednesday morning, and we've obviously got a number to come back this afternoon after the internationals. Touch wood, they'll all come out of that quite well.
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"The players are looking fit, they look strong, and the intensity in their work has been very, very good."
Three points against West Brom is a must for Rodgers as he looks for a strong start to life as Liverpool boss in the face of a tough opening run of matches.
A trip to Sunderland is sandwiched between home ties against Manchester City, Arsenal and Manchester United in the four fixtures following the game against Steve Clarke's side.
And Rodgers has moved to quell expectations ahead of the run, stating that a weak start to the season does not necessarily lead to a weak finish.
"It's good to start well - but it's more important you finish well," he insisted. "You saw last season with Arsenal, they didn't get off to the best of starts in the first 10 games, but they ended up getting into a Champions League spot, which is where they wanted to be.
"For us, of course we ideally want to start well, but it's not the be all and end all if we don't. The most important thing will be where we finish, and I believe the group will get stronger and stronger as the year goes on as they become more attuned to my methods and management."