The Royals have agreed a fee for the Irishman's services with Wimbledon's administrators. Reading MAD believe the deal will be worth around £500,000.
If all goes according to plan the deal should be completed before the team return to pre-season training next week.
Royals Chief Executive revealed that he expects to begin negotiations with Connolly's representatives shortly.
"We've spoken to Wimbledon's administrators and agreed a fee so the initial bit is done. We are now trying to arrange a meeting with his agent to find some common ground over his salary," said Howe, speaking to Reading World.
Norwich and Sunderland were also reported to have shown an interest but baulked at the asking price.
Despite being troubled by niggling injuries Connolly amassed an impressive twenty-four goals in just twenty-eight first division appearances for the Dons last season.
If the Royals were to sign such an experienced and trigger-happy star it would likely see their promotion odds slashed.
The 26-year-old has previously played in the First Division for Watford and Wolves prior to his spell with Wimbledon. Furthermore, he has spent a successful few years in Holland, scoring fifty-five goals on the continent.
Reading have already confirmed that they have agreed a fee for Scott Murray so the Madejski Stadium outfit could very soon have two new recruits.