The 32-year-old has featured as a trialist in a closed-door match with Romanian side Concordia Chiajna and in Saturday's Renfrewshire Cup final against St Mirren.
Rutkiewicz started his career at Aberdeen before departing to begin a seven-year spell at St Johnstone - where he played alongside Ton left-back Willie Dyer.
The experienced centre-half then endured an injury-ravaged stretch with Dunfermline, but Moore is confident he will prove a valuable addition once he completes the paperwork.
Moore told the Tele: "We are hoping to get him tied up by the end of the week.
"We have discussed terms and it's now just a case of the chairman okaying it.
"He would be a good addition to the squad there is no doubt about that - if we can keep him injury-free then he will be a good bonus for us.
"He gives us good experience as well. Big Mark McLaughlin gave us that on Saturday and Craig Reid also did very well for us in the first 45 minutes alongside him in defence.
"If we can get Kevin in, then that bodes well for us. We need cover in the centre of defence, and that is something we lacked last season.
"We have a couple of boys at left-back and right-back who have good legs and then have Martin Hardie ahead of them who has a lot of experience.
"That gives us a good spine in the team, with Derek Gaston having another really good game in goals on Saturday. Kevin would definitely add to that."
The majority of the Ton squad reported for training on Sunday morning - although a number were dispatched to take part in a pre-season tournament against Kilbirnie Ladeside.
He added: "We won 4-2 and Archie Campbell got a hat-trick so that will give him a wee bit of a confidence boost ahead of the season.
"The competitive matches start at the weekend so things are shaping up nicely ahead of that and hopefully we can make a positive start."