I've seen a few different numbers being thrown around for the current Bruins cap space. Here's where I think they stand.
12 Forwards: Krejci ($7.25M), Bergeron ($6.875M), Marchand ($4.5M), Eriksson ($4.25M), Beleskey ($3.8M), Kelly ($3.0M), Hayes ($2.3M), Connolly ($1.025M), Spooner ($950k), Pastrnak ($925k), Talbot ($900k), Rinaldo ($850k)
$36.625M
6 Defensemen: Chara ($6.916667M), Seidenberg ($4.0M), Krug ($3.4M), McQuaid ($2.75M), K. Miller ($800k), Trotman ($625k)
$18.491667M
1 Goalie: Tuukka Rask ($7.0M)
$7.0M
1 Retained: Milan Lucic ($2.75M)
$2.75M
Performance Bonus Overage: $969k
$969k
12 Forwards, 6 Defensemen, 1 Goalie Total: $65.835667M
Current Cap Space: $5.564333M
The Bruins will most likely carry 13 Forwards, 7 Defensemen and 2 Goalies during the regular season. Right now, it seems like Joonas Kemppainen ($792.5k) + Colin Miller ($602.5k) + Jeremy Smith (600k) will fill out the roster.
13 Forwards, 7 Defensemen, 2 Goalies Total: $67.830667M
Projected Cap Space: $3.569333M
As Dom (and others) has pointed out, the Bruins are going to want to bank some cap space going into the season. There's also the possibility that Sweeney will decide to add an experienced backup goalie.
If Franson is close to signing, I think they'd like to move at least $2.5M off of the current team in order to accommodate Franson + a possible backup goalie signing + moving forward with some available space.