Any players that you signed to just 1 year contracts previous season you will not be able to offer them new contracts until next season and other teams will also as they will become FA. The only time I think during off season you cant have contracts accepted is during the Draft, you can still make offers but none will be accepted until draft is over, this includes resigning your own players. Sundays nothing happens but again I believe you can still make offers on Saturdays and Sundays.
Another thing also to keep in mind is if you think one of your players is being paid more then his worth you may be able to renegotiate his contract to open more cap space. The contract has to equal at least how many years he currently is signed for but there are instances where this could save you millions on that player. I usually check this towards the end of the season and revisit beginning of next season.
Hope this helps