The New Lanark pioneer improved the lives of families in mill villages during the industrial revolution through education and humane working practices.
Welsh-born Owen was considered ahead of his time, abolishing child labour and corporal punishment, and providing villagers with free healthcare and affordable food. He died in 1858 at the age of 87.
His belief in co-operative principles and equality for all have already been commemorated with the granting of Unesco status to the New Lanark World Heritage site, an 18th-century cotton mill village in Lanarkshire.
Labour MSP Bill Butler is calling for Mr Owen's face to grace banknotes in time for the United Nations Year of the Co-operative in 2012. The Glasgow Anniesland MSP said: "Robert Owen is respected across the globe and embodies the principles of co-operation and putting people before profit.
"Banknotes already celebrate the contribution of Robert Burns, Walter Scott and Mary Slessor. Now we have a unique opportunity to honour a true visionary whose co-operative ideals remain relevant today.
"I am very pleased that so many colleagues from other parties have backed my motion. . We have sufficient support for it to be considered for debate and together we can make this happen."
Mr Butler has lodged a motion with the Scottish Parliament asking MSPs to support the Bank on Owen campaign.
Lorna Davidson, acting director of the New Lanark Trust, said: "Owen's pioneering social and educational reforms are internationally recognised, as New Lanark's World Heritage Site status clearly demonstrates.
"It would be timely for Scotland's banks to recognise the huge contribution he made to building a better and fairer society."