But Wanderers have been priced out of the market for Swedish striker Johan Elmander.
Steinsson, previously a target for Middlesbrough, has been discussing personal terms before finalising his move from Dutch side AZ Alkmaar.
The 26-year-old right back previously played in Switzerland for Young Boys Berne.
And if he proves as successful at Bolton as compatriots Gudni Bergsson and Eidur Gudjohnsen then Wanderers will have done well.
Manager Gary Megson admitted an interest in Toulouse marksman Elmander last week.
But after the derby defeat by Blackburn, he said: "We went for one player last Saturday and we were quoted 50 percent more than we got for Nicolas Anelka.
Capture
"There is not a great deal you can do about those things."
Harry Redknapp's decision to stay at Portsmouth could speed up the expected capture of Matty Taylor.
Sunderland are tracking the former England under-21 international but Wanderers have an agreement with Pompey.
One reunion unlikely to take place is with West Brom left back Paul Robinson.
The tough-tackling defender, sent off against Hull on Saturday, has been linked with Bolton but Baggies boss Tony Mowbray says: "There has been no contact whatsoever.
"I have had a good conversation with Paul Robinson and he is very determined and focused to make sure this club gets out of this league.
Frenchman Gerald Cid has spoken for the first time after completing his move to La Ligue side, Nice.
"I am happy because I wanted to return to France in the transfer window," he says.
"I didn't play much in England but I discovered a new country, a new league and it is an important step for me."
Hearts' Senegal defender Ibrahim Tall, 26, and Valencia `s Serbian giant, Nikola Zigic are the latest possible targets.
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I am what you would call a long time supporter. I can remember going to Burnden Park to see Alf Ramsey play for Spurs, right back I think. I say this only to illustrate my point that the owners of the Wanderers, who ever they may have been , have all had the same objective ie. take what- ever you can, invest as little as possible, only when absoluty necersary, and rely on the loyalty of the few and hope they don't notice.
Last Saturday, Bolton played with one striker and no other striker on the bench, bear in mind we are the home team. This must be the first time in the history of the premership that this has happened.
The board knew last May that Anelka would be going and Dueif (?) would not be unavailable. What do they do ?. Nothing.
Over the last few years they have got away with not investing and due to good luck and Alladyce's abillity to sniff out a decent player other teams would not look at have attually been reasonably successful.
Alladyce left because the chairman would not invest- the reason always trotted out 1) We must not do a Leeds
2) We are £40mill. in debt (evidence please)
I can only assume Megson was given the job was because he agreed to go along with the no investment rule and stick with rules 1) and 2)