Al-Habsi is out of contract with current club Lyn later this year and is expected to sign a pre-contract with Bolton on Monday.
The 23 year old has been interesting Manchester City lately and this news will be a big blow to Stuart Pearce as he tries to capture cover for David James.
Harrison said on skysports.com, "Bolton have made him an offer. It is for three and half years and I have relayed it to Ali.
"He's thinking it over and he'll probably decide on Monday, but it looks like he is going to Bolton."