The 26-year-old midfielder is believed to be the Reds’ top target for the coming months, and has been the subject of multiple offers – the latest worth around £25m.
But with an agreement yet to be reached, the door has been left ajar for other sides.
One club to have been linked with Lallana is Tottenham, with speculation having been further fuelled by Mauricio Pochettino’s move from the management post at St Mary’s Stadium to the role in the Spurs dugout.
However, it is now understood that the Londoners are not interested in the England international.
Reports suggest that Pochettino will instead work with the talent already at White Hart Lane, much of which was drafted in during the club’s £110m spend last summer.
Liverpool are said to be desperate to snap up Lallana before he jets off to the World Cup, but a move may be complicated by the Three Lions’ impending warm-up trip to Miami.
The Merseysiders are also on the verge of announcing Rickie Lambert’s arrival from Southampton.