Manziel, who has been projected as a first-round pick, is scheduled to fly to Jacksonville on Tuesday and will visit with the Jaguars the following day, according to the source.
The Jaguars also will meet with former Buffalo linebacker Khalil Mack and four other quarterbacks -- Blake Bortles, Teddy Bridgewater, Derek Carr and Jimmy Garoppolo -- this week, according to sources. Jacksonville owns the third overall pick in next month's draft.
Bridgewater is also scheduled to visit the Vikings next Monday and Tuesday.
Mack, who was tabbed as the No. 1 overall pick in ESPN NFL draft expert Mel Kiper's latest mock draft, also will visit with the St. Louis Rams later this week, the source told Schefter. The Rams own the second overall selection.
Manziel was projected as the No. 8 overall pick to the Vikings in Kiper's latest mock draft and was ranked as the No. 20 overall draft prospect by ESPN's Todd McShay.
Bortles, Bridgewater and Carr all have been tabbed as first-round draft picks, while Garoppolo has emerged as a top-10 quarterback prospect, according to both Kiper and McShay.
The Jaguars went 4-12 under first-year coach Gus Bradley in 2013, their third consecutive losing season.
ESPN NFL Insider Ed Werder contributed to this report.