Team boss Chris Morton met the 29-year-old after he finished fifth in the Grand Prix Challenge final in Zielona Gora, Poland, on Sunday.
Jedrzejak claimed 11 points and one more would have put him in a race-off for a place in next year's World Championship.
His performance also caught the eye of injury-hit Elite League club, Lakeside, who have been given permission by the Aces to sign him on loan until the end of the season.
Morton said: "I was very impressed with Tomasz and had a chat with him after the meeting. He is looking to come back to race in England next season and he is one of our options. He is a Belle Vue asset and anyone on our books will be considered. Tomasz has a strong case as he is almost a Grand Prix rider and would be a good signing as he is only on a five-point average."
Jason Crump, Belle Vue's number one, admitted his season is at a low point after seeing his world title dream virtually ended in Saturday's Polish Grand Prix in Bydgocsz.
Crump had to finish ahead of current leader Nicki Pedersen, to have a chance of claiming his third championship.
But he hit problems and the meeting turned into a nightmare with him collecting just nine points to finish eighth and leave Denmark's Pedersen with a 28-point lead with just two GPs to go.
Crump said: "I went to Poland well prepared but the night was a disaster. It virtually blew my chances of winning the world title, but my hold on second place is now under serious threat from Greg Hancock and Tomasz Gollob.
"Two weeks ago I was celebrating my win in the Latvian GP and now I'm at my lowest point."
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