The former Liverpool striker's availability has been known all summer but has so far not secured a deal. His injury record remains an issue and his return might not be welcomed by many fans after his spell with Manchester United. Turns 33 in December.
Another ex-Red without a club, the bustling front man appears to be very much in the mould of Andy Carroll, who was sent out on loan to West Ham United as he did not fit into Rodgers' system. Will be 35 in January.
As with Heskey, Beattie would seem to be a similar style player to Carroll. The striker is available after leaving League One Sheffield United. But having struggled in his latter days at Stoke City and Rangers, the 34-year-old seems unlikely.
The former England international is without a club after leaving Leicester City. But a serious knee injury wrecked his last campaign and there will remain doubts about the 32-year-old's fitness.
As a two-time Everton player, the Scot would represent a controversial choice for Liverpool. McFadden has also suffered a knee ligament injury during his career and could represent a fitness gamble similar to Vassell.
ALESSANDRO DEL PIERO
The veteran's move to Sydney FC appears to have stalled, although whether the former Juventus forward would even consider a switch to Merseyside a couple of months ahead of his 38th birthday is another matter. He has also been linked with Olympiakos.
Former Chelsea and Barcelona forward, who is 34 in September, has the necessary CV to potentially fit into Rodgers' plans but having flopped on his return to the Premier League with Tottenham Hotspur, Stoke City - where fitness was an issue - and then Fulham, another comeback seems unlikely.
Who should Liverpool look to sign from the free agent options?