Approval from the U.S. Federal Trade Commission could come as soon as this week or next, said the sources, who spoke anonymously to protect business relationships.
European antitrust enforcers approved the deal in November on the condition that the companies divest two devices used in cardiovascular treatments.
It was not immediately known what conditions the FTC would require but Abbott said in October the companies would sell some of their medical devices to Japan-based Terumo for about $1.12 billion as a step toward completing the deal.
St. Jude has been under pressure after short-seller Muddy Waters and research firm MedSec Holdings alleged in August that its heart devices were riddled with defects that make them vulnerable to cyber hacks. St. Jude has denied the allegations and sued both firms.
In October, St. Jude said it had notified doctors to stop implants of one of its cardiac pacemakers, the Nanostim leadless cardiac pacemaker, citing reports of problems with electronic data reporting caused by a battery malfunction that could put patients at risk.
There have been no reports of patient injuries associated with the malfunction, St. Jude said.
bbott has been divesting businesses to focus on its cardiovascular devices and diagnostics business, selling its medical optics division to Johnson & Johnson for $4.3 billion earlier this year. It spun off its pharma business as AbbVie in 2013.
Abbott is trying to pull out of a second deal, a $5.8 billion dollar acquisition of diagnostic test maker Alere after Alere failed to file financial statements and disclosed probes into billing and foreign sales practices. The two companies are suing each other.