The Spartak Moscow midfielder was shown around the club's training base on Friday morning while his representatives finalised a loan deal with the Gunners.
Arsenal have agreed a deal to take Kallstrom until the end of the season and pay a loan fee to Spartak.
The Londoners are hopeful of signing the Swede before the 11pm transfer deadline as they close in on two new signings.
As revealed by Footb-INFO, Arsenal are also negotiating a deal with Lazio to take striker Miroslav Klose on loan until the end of the season. Arsenal contract fixer Dicky Law is in Italy to finalise a deal for veteran German striker Klose.
The Gunners have lined up Real Madrid youngster Alvaro Morata as an alternative if they cannot finalise terms with Lazio for Klose but they are increasingly confident of landing the prolific 35-year-old.
As revealed on Tuesday, Aaron Ramsey is out for up to six weeks after sustaining a fresh thigh injury in training and Wenger decided to reinforce his central midfield.
The Arsenal boss moved for Kallstrom after learning that first-choice target Blaise Matuidi will extend his Paris Saint-Germain contract and being put off by Southampton’s £15 million valuation of Morgan Schneiderlin.
