Methods based on the use of multivariate autoregressive models (MVAR) have proved to be an accurate tool for the estimation of functional links between the activity originated in different brain regions. A well-established method for the parameters estimation is the Ordinary Least Square (OLS) approach, followed by an assessment procedure that can be performed by means of Asymptotic Statistic (AS). However, the performances of both procedures are strongly influenced by the number of data samples available, thus limiting the conditions in which brain connectivity can be estimated. The aim of this paper is to introduce and test a regression method based on Least Absolute Shrinkage and Selection Operator (LASSO) to broaden the estimation of brain connectivity to those conditions in which current methods fail due to the limited data points available. We tested the performances of the LASSO regression in a simulation study under different levels of data points available, in comparison with a classical approach based on OLS and AS. Then, the two methods were applied to real electroencephalographic (EEG) signals, recorded during a motor imagery task. The simulation study and the application to real EEG data both indicated that LASSO regression provides better performances than the currently used methodologies for the estimation of brain connectivity when few data points are available. This work paves the way to the estimation and assessment of connectivity patterns with limited data amount and in on-line settings.