The England international pulled out of the Three Lions squad that was set to face Lithuania and Italy after suffering a tear in his hip flexor muscle during Liverpool's defeat to Manchester United on March 22.
It was initially reported that Sturridge would be out of action for up to a month, but the Reds medical staff are believed to feel that he could recover a lot sooner, with Saturday's clash with the Gunners not necessarily a bridge too far.
Brendan Rodgers' side will be without the services of the suspended Steven Gerrard and Martin Skrtel for the match, while Adam Lallana is an injury doubt. As such, the surprise availability of Sturridge would come as a massive boost.
The 25-year-old striker has endured a horror run of injuries this season, spending half of the campaign on the sidelines. Two thigh injuries either side of a calf problem have meant that the Reds have had to do without their much-needed attacker for considerable periods.