Police chiefs said they had been "let down" by the government after not receiving enough cash for new officers.
Police chiefs say they must find the cash elsewhere
Humberside Police Authority said it had only been given funding to recruit two-thirds of the community support officers it needed over the next year.
It said that instead of employing 332 extra officers, the Home Office had only given it the funding for 210.
Authority officials said they could have to make cuts elsewhere to find the cash for the other 122 officers.
The cost of keeping the 122 extra officers on the streets for the next five years is estimated at £11.3m.
'Let us down'
Police authority chairman Graham Stroud said: "Although we feel that the government has let us down on this, we are examining every option open to us so that we can fund the programme out of our existing budget.
"This is not an easy task as we do not wish to do this at the expense of frontline performance.
"We have to be certain that even if we manage to find enough room in the current budget that we can carry this through in years to come. We certainly have the will to do this, now we just need to find the way."
A Home Office spokeswoman said the government had increased its funding for police officers and community support officers by 45% for the next financial year.
She said that meant across the country there would be an extra 16,000 community support officers.
She said: "We do not expect forces to increase that number although they can if they wish to do so."
Police authority leaders said they would continue discussions with the Home Office.
A final budget, including how much it will require from council tax, will have to be agreed on 13 February.