The club have been tracking the 24-year-old for over a year, after discovering his Jewish ancestry and is able to join the squad without counting towards overseas quotas, and have lodged several offers to lure him to Haifa.
The goalkeeper, who recently enjoyed a loan spell at Hull City, is also of interest to Reading but remains unwilling to drop down to League One after two seasons in the Championship along with previous experience in the Scottish Premiership with Ross County.
The 15-time Israeli champions can offer Baxter a run in the Champions League and are keen to wrap up a deal before their first-round qualifier in the middle of July.
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Baxter, who was born in London to parents of Jewish descent, has played over 200 senior matches and won a host of youth trophies at Stamford Bridge.
He will leave, however, having not played a senior match for Chelsea after 17 years with the club.
