The decay phi -> f(0) (980)gamma and process e(+) e(-) -> phi f(0) (980) are considered within the local Nambu-Jona-Lasinio model. In the amplitudes of these processes, contributions of s-quark and kaon loops are taken into account. The kaon loop gives a dominant contribution. Our estimation for the decay width of phi -> f(0)gamma is in satisfactory agreement with recent experimental data. This allows us to make some predictions for cross sections of the process e(+) e(-) ->gamma* -> phi f(0) which can be tested in the C-tau factory. The total and differential cross sections of this process are calculated and presented in the figures.
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