We report on a new method suitable for the fabrication of highly sensitive SQUID magnetometers exhibiting very small effective areas. In contrast to commonly used approaches, which mostly make use of constrictions in a superconducting material to form the Josephson junctions, we have been able to fabricate such sensors with SIS cross-type Josephson tunnel junctions in an Nb/AlOx/Nb trilayer process. The small junction size and vanishing idle region of our cross-type junctions and a therefore very low capacitance lead to a high sensitivity of the resulting SQUIDs. First results on fabricated miniature SQUID magnetometer within this technology are shown, which demonstrate the capability of our approach. Furthermore we estimate the required SQUID parameter which may allow the detection of single electron spin-flips with such devices in the future.