Bruce has reluctantly confirmed that he hopes to sign the versatile 27-year-old Czech Republic schemer on a deal similar to that of recent signing Nicky Butt - that being a season long loan deal with a view to making the move permanent at the end of that agreement.
"I hate talking about players contracted to other clubs," Bruce told Sky Sports News.
"However, its come out in the media, as these things often do these days. We have made an enquiry and it's a possibility.
"We have a good relationship with Chelsea so I hope a deal can be done because he is a player I admire."
The deal to bring Jarosik to Blues is likely to depend on the Michael Essien transfer from Lyon to Chelsea being concluded. Essien is currently discussing personal terms over a £26 million move to Stamford Bridge.