Swindon boss Danny Wilson said last week he was hopeful of concluding a deal for Obika.
"He's still Peterborough's player this moment in time but we're hopeful we'll have an addition next week some stage," Wilson told BBC Wiltshire on Friday.
He added: "It's not done and dusted as he's still technically a Peterborough player."
Obika played for Spurs in their UEFA Cup campaign during the 2008/09 season but since then has spent time on loan with Millwall and Yeovil (twice).
He arrived at London Road four weeks ago having had a four month spell at Crystal Palace at the start of this season.
Source: BBC Sport
Source: BBC Sport