Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The 27-year-old midfielder is currently working under a season-long agreement sanctioned by parent club Norwich City.
It would appear as though his days at Carrow Road are numbered, with no talks held regarding an extension to a contract which is due to expire in the summer.
If no deal is put in place, Surman would be dropped into the free agent pool.
He would then be able to decide on his next move, and an extended stay at Bournemouth is something that would appeal to him.
Surman told the Daily Echo: "Having signed on loan for the season I knew I was going to be here, which helped me to settle in and I have really enjoyed it.
"Maybe we need to re-evaluate what's best for me and the club, but with January gone we probably wouldn't be discussing anything concrete until the summer.
"It's just a case of having in mind what I want to do next season and I will have to see what Norwich say as well because I'm not sure what their intentions are at this stage. It's all up in the air.
"If it was right for everyone, of course I would be open to it (staying with the Cherries).
"It just depends on where things are when the summer comes round because I know I have got a few decisions to make."