The company has announced plans for around 2,400 job cuts in Finland and Germany as part of a cost-cutting programme but has not so far given a global figure.
Cuts on the scale estimated by the union would represent as much as 14% of Nokia's worldwide work force of 104,000.
Nokia kicked off the rationalisation programme in April with a target to slash 900 million euros ($1 billion) of operating costs by 2018.
"We haven't heard any official numbers, but based on the information from our union contacts, I would estimate the global impact of this round would likely be around 10,000 to 15,000 jobs," said Risto Lehtilahti, a trade union shop steward at Nokia's Oulu site.
A Nokia spokeswoman declined comment on the figure.
Analysts and union representatives said that the company will likely follow up with a new round of cuts once the current one is finished.
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"Nokia and Alcatel have lots of overlaps, so the numbers will go up and the range could be something like that (10,000-15,000)," said Hannu Rauhala, analyst at OP Equities.
"The integration takes place at a very hectic stage in the network industry. The market is falling, technology is changing and the environment is turbulent, so it is difficult to see that they would make it (the company) ready in one go," he said.
Nokia set out plans for its home country last week, saying it was cutting around 1,000 Finnish jobs, compared to an initial target of 1,300 jobs.
Nokia has said it is looking to reduce 1,400 positions in Germany. In France, it would cut around 400 jobs but also create 500 research and development posts.
To win French government support for the 15.6 billion euro deal, Nokia pledged during negotiations not to cut French jobs for two years, beyond what Alcatel had already planned.
The Nokia spokeswoman said the company didn't have any updates for France or Germany, and declined to give details on other countries. Nokia is holding talks with employee representatives in about 30 countries.
The savings plan is partly due to tackle the weak network gear market. Nokia forecast earlier this month that its network sales would fall this year.
"Some work will be completely terminated, some cuts come from Alcatel overlaps, and some work will be transferred to countries with lower costs," said Tuula Aaltola, another Finnish shop steward.
The market leader, Sweden's Ericsson, is also cutting costs as tough competition pressures network gear prices.
According to Communication Workers of America (CWA), Nokia started to reduce U.S. jobs a year ago in preparation for the merger.
"We don't know what Nokia's plan is for the U.S.-based workforce. They have cut 500, cut our (unionised) workforce in half, and we hope that's all that is going to be taken away," CWA representative Lisa Bolton said.
In Finland, Nokia has slashed thousands of jobs over the past decade as its once-dominant phone business was eclipsed by the rise of smartphone rivals. The phone business was eventually sold to Microsoft, which has continued cutting jobs in the country. ($1 = 0.8924 euros)