The 24-year-old, who would be available for no fee at the end of his contract this summer, has already held talks with Jewell and undergone a medical at Pride Park.
The Rams boss told www.dcfc.co.uk: "Paul is available on a Bosman in the summer so we spoke to (Plymouth boss) Paul Sturrock to ask permission to talk to the player."
He added: "We have done that and hopefully we can conclude a deal pretty quickly. He is keen to come and fits the bill as he is 6ft 1in, athletic and hungry.
"Paul is a fighter, and that is what I want to bring, as well as quality, which he has got."
Connolly joined Argyle as a trainee and, after making his first team debut in 2001, has racked up 177 appearances for the Pilgrims.
Jewell has declared his intention to completely revamp the squad following their dire season in the Barclays Premier League and has already secured the services of Australian midfielder Ruben Zadkovich.