Queen of the South played Nordsjaelland at Excelsior Stadium
Motherwell could ask near neighbours Airdrie United to host their Europa League qualifying tie should they win a place through the Fair Play League.
The Fir Park pitch is undergoing extensive remedial work this summer.
And the ground, the condition of which was heavily criticised this season, will not be ready for the beginning of July, when the tie will take place.
If Motherwell claim a place in Europe, the two-leg tie will be played on 2 and 9 July.
Airdrie's Excelsior Stadium would be ideal as it is a 10,170 all-seated arena.
It is a stadium approved by European football's governing body, having played host to Queen of the South's Uefa Cup tie against the Danish side Nordsjaelland in August.
Other stadia that could be considered are Hamilton Acacemicals' New Douglas Park and Livingston's Almondvale. However, Accies' ground only holds 6,078.
Motherwell lead the way in the Fair Play table of the teams not already qualified for Europe. St Mirren and Hibernian are their nearest challengers.
Work begins at Fir Park on Sunday to help improve the playing conditions.
The surface will be dug up and replaced - and the undersoil heating system will be repaired.
Motherwell's first match at Fir Park after the work is complete will be a pre-season friendly against Wigan Athletic on Saturday 8 August.
That will be the last warm-up game before the start of the 2009/10 Scottish Premier League season and the only one on home soil due to the remedial work on the pitch.
It will be the second successive season Wigan have visited Scotland as part of their pre-season preparations.
Last year, they faced Hibs at Easter Road and won 1-0 with a goal from Amr Zaki.
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