The deadline day addition is yet to feature for the Gunners since signing, and despite reports he could feature against Everton last weekend, he was nowhere to be seen.
Recovering from a back injury, the Swedish international was not photographed in training ahead of the Bayern Munich game on Monday, and did not travel to Germany.
His potential return could have even more significance, because a key player hoped to be back in contention to feature against Spurs is unlikely to play any role.
The paper report that Aaron Ramsey, the standout player in the Premier League during the first quarter of the season, is 'expected to miss out'.
Ramsey has not featured since late December, struggling with a thigh injury which he aggravated during January when he was thought to be nearing a comeback.
While always perhaps a 'hope' that he would be back for the Spurs game, it had been widely reported that the Welshman was targeting the crucial fixture as a potential return date.
Midfielder Jack Wilshere is also out injured with a fractured foot, and Mesut Ozil is expected to miss a month with an injured hamstring, with Theo Walcott a long-term absentee.
At left-back Arsenal have a dilemma, with Nacho Monreal winning his fitness battle, but Kieran Gibbs not - but Arsene Wenger's decision rests with whether to stick with Thomas Vermaelen who did well against Bayern in midweek.
In midfield the Gunners do have options despite the injuries; Alex Oxlade-Chamberlain is a must-start, while Mikel Arteta and Mathieu Flamini should begin the game at White Hart Lane.
Santi Cazorla is likely to move into the centre in place of Ozil unless Oxlade-Chamberlain features there, with Tomas Rosicky and Lukas Podolski vying for positions.
Despite the injuries, Arsenal's midfield squad depth is still strong, and Kallstrom can hope for at best a place on the substitute's bench this weekend.