The Southampton captain is reported to have undergone a medical at Melwood on Saturday ahead of his £23m switch to Anfield from the south coast club.
I wouldn’t be concerned Liverpool are being left behind. It’s still early days
Lallana, who scored nine goals and made six assists in 38 Premier League appearances, is the Reds’s third summer signing after Rickie Lambert and Emre Can.
But Lawrenson is tipping Liverpool, who have been linked with Dejan Lovren and Alexis Sanchez in recent days, to further strengthen their squad ahead of the new season.
“Manchester United are making big moves in the transfer market,” Lawrenson wrote in his Liverpool Echo column.
“But I wouldn’t be concerned Liverpool are being left behind. It’s still early days.
“And, with Adam Lallana on his way to follow Rickie Lambert and Emre Can, the Reds have been more than busy.
“In any case, July is the month when, with everybody back in pre-season training and the manager physically making plans for the start of the new campaign, matters begin to pick up.
“The transfer market is always a bit funny during a World Cup year. Teams are having to wait until players aren’t involved in the tournament, as has happened with Lallana.
“The Southampton midfielder won’t be the last signing, although a move for Alberto Moreno appears to have stalled.”
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