The Reds completed a £15m deal for the Swansea City midfielder last Sunday, and Rodgers – who previously coached Allen at the Liberty Stadium – is considering handing the Team GB star his first Liverpool start at the Hawthorns.
“Yes [Allen is in contention],” Rodgers told Liverpool’s website. “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.”
The 39-year-old is confident his Liverpool squad will reap the benefit of the two Europa League games against Gomel, which saw the Reds progress into the play-off round courtesy of a 4-0 aggregate victory.
“I believe it has narrowed our focus into a competitive element,” he added.
“The games in pre-season are about fitness, but certainly when you turn the screw and go into the Europa League games and then the league, you see that real competitive nature come out in the players. I felt the two games [against Gomel] helped us in that way.
“The players are ready and their mindset is to compete. Hopefully we can continue with the good momentum we’ve built over the course of pre-season.
“Looking at the game against Gomel last Thursday, we had nearly 70 per cent of the ball and we made over 740-odd passes in the game, which tells you the team is in good condition and control.
“Then we played a very good side in Bayer Leverkusen at the weekend and had a positive result and performance.
“The shape and mentality of the team is in a good moment and we can’t wait to get started.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news