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NFL teams don't generally publicize which prospects they are meeting with for obvious reasons, but that's not to say the information isn't out there.
SB Nation is keeping a running prospect visit tracker for all 32 teams, as is WalterFootball.com. CBSSports has an unofficial list of the players that actually met with the Bears. The Bear Report's Aaron Leming has a prospect visit spreadsheet that he constantly updates for the players meeting with the Bears. You can also run a "#Bears" Twitter search or a good old fashioned Google search to find some info.
The Chicago Bears had representatives at most of the big college pro days and they also hosted a local pro day for players with ties to the Chicagoland area.
So besides the various pro days, the Bears could have met with prospects at the NFL Combine, the East West Shrine Game, the Senior Bowl and they could have set up a private workout/meeting with prospective players as well.
So by compiling all the data above, here's where the Bears stand on pre-draft visits. I'll group them by position and include the projected draft round from CBSSports.
Reminder: This list consists of every prospect that the Bears have spoken with, not only pre-draft visits to Halas Hall.
QUARTERBACKS
1st round, Jameis Winston (6'4", 231), Florida State
1st round, Marcus Mariota (6'4", 222), Oregon
3rd round, Bryce Petty (6'3", 230), Baylor
3rd/4th round, Garrett Grayson (6'2", 213), Colorado State
UDFA, Taylor Graham (6'5", 235), Hawaii,
UDFA, Matt Behrendt (6'1", 200), Wisconsin-Whitewater
UDFA, Chandler Whitmer (6', 200), Connecticut
UDFA, Trevor Siemian (6'3", 220), Northwestern
RUNNING BACKS
1st round, Todd Gurley (6'1", 222), Georgia
2nd round, Tevin Coleman (5'11", 206), Indiana
6th/7th round, Malcolm Agnew (5'9", 202), Southern Illinois
7th round, Dominique Brown (6'2", 234), Louisville
WIDE RECEIVERS
1st round. Amari Cooper (6'1", 211), Alabama
1st round, Kevin White (6'3", 215), West Virginia
1st round, DeVante Parker (6'3", 209), Louisville
1st round, Breshad Perriman (6'2", 212), Central Florida
4th round, Tony Lippett (6'2", 192), Michigan State
7th round/UDFA, Deon Long (6', 193), Maryland
UDFA, DeAndrew White (5'11", 193), Alabama
UDFA, Christion Jones (5'10", 182), Alabama
UDFA, Kyle Prater (6'5", 231), Northwestern
TIGHT ENDS
4th round, Tyler Kroft (6'5", 246), Rutgers
7th round, James O'Shaughnessy (6'4", 248), Illinois State
7th round/UDFA, E.J. Bibbs (6'2", 258), Iowa State
UDFA, Matt LaCosse (6'6", 257), TE, Illinois
OFFENSIVE LINEMEN
1st/2nd round, D.J. Humphries (6'5", 307), OT, Florida
1st/2nd round, T.J. Clemmings (6'5", 309), OT, Pittsburgh
6th/7th round, Max Garcia (6'4", 309), C/OG/OT, Florida
UDFA, Arthur Ray Jr. (6'2", 292), OG/OT/C, Fort Lewis
UDFA, Cornelius Edison (6'3", 307), C, Portland St
DEFENSIVE LINEMEN
1st round, Danny Shelton (6'2", 339), NT, Washington
2nd round, Mario Edwards Jr. (6'3", 279), DE/OLB, Florida State
UDFA, David Irving (6'7", 273), DE, Iowa State
LINEBACKERS
1st round, Vic Beasley (6'3', 246), OLB, Clemson,
1st round, Dante Fowler Jr. (6'3", 261), OLB, Florida
1st round, Randy Gregory (6'5", 235), OLB, Nebraska
1st round, Shane Ray (6'3", 235), OLB, Missouri
1st round, Alvin Dupree (6'4", 269), OLB, Kentucky
1st/2nd round, Eli Harold (6'3", 247), OLB, Virginia
2nd round, Benardrick McKinney (6'4", 246), ILB, Mississippi State
2nd round, Nate Orchard (6'3", 250), OLB, Utah
7th round, Junior Sylvestre (6', 233), LB, Toledo
DEFENSIVE BACKS
1st round, Trae Waynes (6', 186), CB, Michigan State,
1st round, Byron Jones (6'1", 199), CB/S, Connecticut
2nd/3rd round, P.J. Williams (6', 194), CB, Florida State
2nd/3rd round, Ibraheim Campbell (5'11", 209), S, Northwestern
2nd/3rd round, Cody Prewitt (6'2", 208), S, Ole Miss
6th/7th round, Deshazor Everett (5'11", 188), CB, Texas A&M
UDFA, Corey Cooper (6'1", 211), S, Nebraska
UDFA, Greg Henderson (5'11", 181), CB, Colorado
If you come across any prospects that I haven't listed, just put a link in the comment section and I'll update the list.
Navy long snapper Joe Cardona has also drawn strong interest from Kansas City Chiefs, Chicago Bears, Indianapolis Colts and Vikings
— Aaron Wilson (@RavensInsider) April 23, 2015
No confirmation of discussion between the Bears and Cardona, but I wanted to pass this info along. Here's Wilson's story on Cardona.