However, with the 24-year-old an established first-team regular at St Mary's, he will likely be more tempted by the move that would give him the highest chance of being a starter.
And though Liverpool have more centre-backs in their squad, that chance will almost certainly be larger at Anfield. The reason is a simple one: the partnership of Laurent Koscielny and Per Mertesacker.
|Team||Pos||Goals Conceded||Clean Sheet||Aerial Won||Won Tackle||Effective Clearance||Apps||Mins|
As Opta stats show, the Arsenal duo - who clash later today at the World Cup - played the majority of the Gunners' Premier League campaign last term, where injuries were the main reason for any absences.
The pair kept 16 clean sheets between them, with their side only conceding 25 goals when Koscielny was on-field. Aerially, the experienced Mertesacker reigned supreme, while his defensive partner won more tackles.
As a duo, they don't need replacing. Who might need replacing is Thomas Vermaelen, who could be on the way to Manchester United. The Belgian, though, played the role of a backup player last season, being restricted to just 14 league appearances.
By contrast, Liverpool's centre-backs shared a huge number of games between the four of them. Martin Skrtel was the only real ever-present, while form and fitness meant Rodgers often selected either Daniel Agger, Kolo Toure or Mamadou Sakho.
But the Reds still ended up conceding 50 Premier League goals last term, a figure that often cost them vital points. Should Lovren move to Anfield, then, he'll have a chance to cement himself as a regular partner for Skrtel - or at the very least share a high number of games with Sakho or Agger, depending on if the Dane doesn't leave Merseyside this summer.
The prospect of more playing time is thus a key advantage for Liverpool in the race for the 24-year-old's signature. Though it remains to be seen how much of a factor it will play in negotiations.