Context. MGRO J2019+37 is an unidentified extended source of very high energy gamma-rays originally reported by the Milagro Collaboration as the brightest TeV source in the Cygnus region. Its extended emission could be powered by either a single or several sources. The GeV pulsar AGL J2020.5+3653, discovered by AGILE and associated with PSR J2021+3651, could contribute to the emission from MGRO J2019+37. Our aim is to identify radio and near-infrared sources in the field of the extended TeV source MGRO J2019+37, and study potential counterparts to explain its emission. Methods: We surveyed a region of about 6 square degrees with the Giant Metrewave Radio Telescope (GMRT) at the frequency 610 MHz. We also observed the central square degree of this survey in the near-infrared Ks-band using the 3.5 m telescope in Calar Alto. Archival X-ray observations of some specific fields are included. VLBI observations of an interesting radio source were performed. We explored possible scenarios to produce the multi-TeV emission from MGRO J2019+37 and studied which of the sources could be the main particle accelerator. Results: We present a catalogue of 362 radio sources detected with the GMRT in the field of MGRO J2019+37, and the results of a cross-correlation of this catalog with one obtained at near-infrared wavelengths, which contains ∼3 × 105 sources, as well as with available X-ray observations of the region. Some peculiar sources inside the ∼1◦ uncertainty region of the TeV emission from MGRO J2019+37 are discussed in detail, including the pulsar PSR J2021+3651 and its pulsar wind nebula PWN G75.2+0.1, two new radio-jet sources, the Hii region Sh 2-104 containing two star clusters, and the radio source NVSS J202032+363158. We also find that the hadronic scenario is the most likely in case of a single accelerator, and discuss the possible contribution from the sources mentioned above. Conclusions: Although the radio and GeV pulsar PSR J2021+3651 / AGL J2020.5+3653 and its associated pulsar wind nebula PWN G75.2+0.1 can contribute to the emission from MGRO J2019+37, extrapolation of the GeV spectrum does not explain the detected multi-TeV flux. Other sources discussed here could contribute to the emission of the Milagro source