Manager Frank Lampard said Everton could go into the transfer market to sign another centre-forward with England international Calvert-Lewin likely to miss their first seven games of the season, including the Merseyside derby.
Salomon Rondon is also suspended this weekend after being sent off against Brentford last season, leaving Lampard considering using Alli, who has not scored a Premier League goal, as the spearhead of his attack.
“Potentially,” he said. “He made his name as a second striker to Harry Kane and had some great years at Tottenham. Maybe he moved back at Tottenham to become more of a No 8. When you look at our squad, he is certainly in the running for solutions.
“Losing a player like Dominic, [with] his quality, in the week going into the first game is probably going to affect you. I think we are probably looking at six weeks for the injury. We will have to work around it and other players will have to step up and do the job.
“Dominic was looking great: really fit, really strong. Through pre-season we were constantly commenting on how good he looked. It is a knock for everyone and particularly for him. I feel for him and as a team a squad we have to look at the game ahead of us.”
Lampard has made three signings – centre-back James Tarkowski, left-back Ruben Vinagre and winger Dwight McNeil – but has not brought in a striker since Richarlison joined Tottenham
“It may be an area we look at,” he added, while arguing Everton are not the only club who are short of players as the season starts.
“I don’t think we are the only Premier League team where you might look at a certain area of the pitch and say they are looking for a solution there. When a window goes three weeks into the season, it is not as simple as to say everyone should get their business done early.”
Everton will start the season without the sidelined Andre Gomes and Tom Davies while captain Seamus Coleman will step up his recovery from injury by playing for their Under-21s on Friday.